Refrigeration: Theory And Applications
Bookboon, 2013. — 128 p. — ISBN: 978-87-403-0363-6Refrigeration: Theory and Applications by James K Carson covers the ba
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Refrigeration: Theory And Applications James K. Carson
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James K. Carson
Refrigeration: Theory And Applications
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Refrigeration: Theory And Applications 1st edition © 2013 James K. Carson & bookboon.com ISBN 978-87-403-0363-6
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Refrigeration: Theory And Applications
Contents
Contents 1
Introduction
8
1.1
Importance of Refrigeration
8
1.2
A Brief History of Refrigeration
9
1.3
Scope and Outline of this Book
10
1.4
Bibliography for Chapter 1
10
Part 1: heory
11
2
hermodynamics
12
2.1
Deinitions
12
2.2
he First Law of hermodynamics
16
2.3
he Second Law of hermodynamics
17
2.4
Phase diagrams and refrigerant properties
22
2.5
Vapour Compression Cycles
26
2.6
Cascade and multi-stage vapour compression cycles
37
2.7
Sorption refrigeration
44
2.8
Summary of Chapter 2
47
2.9
Further Reading
48
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Refrigeration: Theory And Applications
Contents
3
Heat Transfer
49
3.1
Modes of heat transfer
49
3.2
Steady state conduction and convection
49
3.3
Heat Exchangers
54
3.4
Transient Heat Transfer
59
3.5
Summary of Chapter 3
65
3.6
Further Reading
66
4
Refrigerants
67
4.1
Desirable Attributes of Refrigerants
67
4.2
Refrigerants ater the Montreal and Kyoto Protocols
69
4.3
Summary of Chapter 4
71
4.4
Further Reading
71
5
Refrigeration without a Refrigerant
72
5.1
Evaporative cooling
72
5.2
Peltier-Seebeck efect (thermoelectric devices)
73
5.3
Magneto-Caloriic Efect (Magnetic Refrigeration)
75
5.4
hermo-acoustic efect (acoustic refrigeration)
76
5.6
Summary of Chapter 5
78
5.7
Further Reading
78
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Refrigeration: Theory And Applications
Contents
Part 2: Applications
79
6
Chilling and Freezing
80
6.1
Estimating Chilling times of food products
81
6.2
Estimating heat loads of food products
88
6.3
Freezing and hawing Time Prediction
88
6.4
Summary of Chapter 6
93
6.5
Further Reading
93
7
Food Refrigeration
95
7.1
he Domestic Refrigerator
95
7.2
he Cold Chain
97
7.3
Typical examples of refrigerated facilities
98
7.4
Design Considerations
101
7.5
Refrigerated transport
104
7.6
Summary of Chapter 7
108
7.7
Further Reading
108
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Refrigeration: Theory And Applications
Contents
8
Air Conditioning
110
8.1
Air-conditioning Cooling Load Calculations
110
8.2
Domestic air-conditioning
113
8.3
Large-scale air-conditioning
115
8.4
Summary of Chapter 8
116
8.5
Further Reading
116
9
Cryogenics and Gas Liquefaction
117
9.1
Cryogenics
117
9.2
Gas Liquefaction
118
9.3
Summary of Chapter 9
119
9.4
Further Reading
119
10
List of Symbols:
120
11
Appendix: Physical Properties of Refrigerant R134a
122
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Refrigeration: Theory And Applications
Introduction
1 Introduction 1.1
Importance of Refrigeration
For most people, certainly in the developed world, the word ‘refrigeration’ would probably evoke the image of a white or metallic-grey device in their homes which is used to keep food and beverages cool. hese devices are generally reliable and low-maintenance and have a familiar, comforting quality, but do not solicit much thought or attention. However, refrigeration goes far beyond the domestic setting, or the supermarket or grocery store where ‘fridges’ are most commonly seen by the average person. he reality is that societies in the developed world depend on refrigeration to the point where it would be no exaggeration to say that many lives would be lost if all mechanical refrigerators were suddenly to fail. In addition to keeping beer chilled, and ice cream frozen, refrigeration is vital for food supply and security, particularly for countries who import the majority of their food (more than 80% in some instances). Nature does not work according to humanity’s schedule; many fruits and vegetables are produced seasonally and refrigeration technology provides us with the ability to store perishable produce in order to balance the irregular supply with the much more steady demand. A number of countries which are signiicant food exporters (e.g. Australia, New Zealand, Chile and Argentina) are geographically isolated from the major food importers (particularly in Europe) and refrigeration provides the means for transporting foods large distances by the relatively slow mode of sea transport. Even within national borders, refrigerated transport is important since, in highly urbanised countries at least, much of the food produced in rural areas is destined to be consumed in the cities. Estimates by the International Institute of Refrigeration suggest that on average 25% of food produced is wasted, due to spoilage during transportation and storage, and much of this (particularly in the Developing World) could be prevented by refrigeration. In fact there is a correlation between the number of refrigeration units per capita and rates of malnutrition. As we head further into the 21st Century, refrigeration is becoming more and more crucial to achieving the goal of feeding a growing population in a world where we have run out of room to expand our crops and pastures. But the importance of refrigeration is not limited to food. hink of a typical hospital: many vaccines, anaesthetics, blood plasma and other forms of medication need to be kept refrigerated; some at temperatures signiicantly lower than that at which most food is stored. Although it has a diferent name, ‘air conditioning’ is mostly the same process as refrigeration. And it is not just human comfort that is at issue – in the 21st century air-conditioning is vital for keeping large computers and data-centres (i.e. ile server banks) producing megawatts of heat, at operable temperatures. Modern society is so dependent on computers that failure in the air conditioning systems that cool the electronic systems that keep all our records, and control so much of the processes we rely on in everyday life, could be catastrophic.
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Refrigeration: Theory And Applications
Introduction
And then there is cryogenics – the science of low temperatures. At low temperatures all sorts of interesting phenomena occur. CERN’s Large Hadron Collider requires temperatures to be low in order for their experiments to be run. Refrigeration provides key support in the pursuit of knowledge about our universe and the workings of nature that we are yet to fully comprehend. his picture of refrigeration has been painted with broad brush-strokes, but hopefully you will see that refrigeration goes beyond the mundane and commonplace role that is associated with the humble fridge, and that it truly is vital technology for our health, longevity and well-being in the modern age. So how did we get to the point where we rely on refrigeration so much? To answer, that question let us look very briely at the development of refrigeration from ancient times. Subsequently we will adopt a deinition of refrigeration as it is used in this book.
1.2
A Brief History of Refrigeration
It is diicult to put a date on the irst ever usage of a cold environment to preserve food, but there is evidence to suggest that the practice is many thousands of years old. Caves appear to have been used to store food (particularly the hunter’s animal prey) in primitive times, and that people in warmer climates were aware that by climbing high hills or mountains the air would be cooler and could be used for food storage. A Chinese poem of 1100 BC mentions a house where ice was stored, speciically for domestic use. In the 5th Century BC the Greek Protagoras reported that the Egyptians were capable of producing ice by placing water on their roofs when there was a clear night sky. Several hundred years later the Roman Emperor Nero Claudius is reported to have sent slaves to the mountains to fetch snow to be used speciically for cooling fruit drinks. As time progressed, ice and snow began to be harvested and traded. During the time of the Roman Empire, citizens of Rome were supplied with ice from the Apennine Mountains. Caravans of camels were used to transport snow from the hills of Lebanon to the Caliphs in Baghdad and Damascus. By the 19th Century the trade in natural ice was intercontinental – in 1899 half a million tonnes of natural ice was imported from the United States and Norway to Great Britain. But there is also clear evidence that these passive means of keeping food cool were not the only ones employed. An Egyptian frieze dated from some 5000 years ago depicts a man waving a fan in front of an earthenware jar, which, it is thought (with support from other sources), would have been illed with water in order to achieve cooling by evaporation. Later on, but possibly as early as the 4th Century AD in India people noticed that certain salts, such as sodium nitrate, when added to water caused cooling efects. By the 16th Century it was well-known that adding these salts to ice would result in temperatures that were lower than that of the ice or snow on its own. It was in 1550 that the irst use of the expression ‘to refrigerate’ (essentially to ‘make fresh’) appears to have been used by Blas Villafranca, who published a text on the subject.
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Refrigeration: Theory And Applications
Introduction
However, the real leap forward in terms of refrigeration technology came with the development of mechanical refrigeration during the 18th and 19th Centuries, which occurred largely as part of the movement to understand heat engines and the wider science of thermodynamics. People began to design devices operating in cycles using a working luid, such as ammonia, to achieve cooling. Names such as Carrier and von Linde (major players in the development of refrigeration) are familiar to many today as brand names on modern refrigeration equipment. he 20th Century saw an explosion in the uptake of mechanical refrigeration, thanks to mass production and the progress in technology (interestingly CFC refrigerants, which until the end of last century were regarded as near perfect refrigerants, are oten credited with a signiicant role in this ‘explosion’). he result, of course, is that refrigerators, air conditioners and heat pumps are common features in homes, shops, oices, hotels and other buildings all around the world.
1.3
Scope and Outline of this Book
his book is concerned with the active, mechanical production of ‘cold’ (note that we don’t really have an antonym for ‘heat’ in the English language). herefore, when the term refrigeration is used, it is not meant to include the use of naturally occurring ‘cold’ from the environment. As a general term, refrigeration also includes air-conditioning technology; however, due to its similarity, heat pump technology will also be covered. he majority of the content of the book is concerned with devices based on the vapour compression cycle, since it is this technology that the vast majority of refrigerators, air conditioners and heat pumps employ. However, other techniques will also be covered, albeit in less detail (see Chapter 5 in particular). he book is split into two parts. Part 1 deals with the underlying physics associated with refrigeration technology (thermodynamics and heat transfer in particular). Part 2 deals with the applications of refrigeration technology, in the ields of preservation (of biological material), human comfort and cryogenics. he book is intended for use as a text for a third or fourth year elective paper (or possibly a taught Masters paper) for engineering students. Prior knowledge of (or at least exposure to) thermodynamics and heat transfer is assumed; however, only basic theory is covered, and some students may be capable of understanding the content without signiicant prior knowledge.
1.4
Bibliography for Chapter 1
Pearson, SF, Refrigerants Past, Present and Future, Proceedings of the 21st International Congress of Refrigeration, Washington DC, 2003 hévenot, R. A history of refrigeration throughout the world, International Institute of Refrigeration, Paris, 1979 5th Informatory Note on Refrigeration and Food, International Institute of Refrigeration, Paris, 2009
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Refrigeration: Theory And Applications
Part 1 Theory
Part 1: Theory 4+
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Refrigeration: Theory And Applications
Thermodynamics
2 Thermodynamics 2.1
Deinitions
It is assumed that the reader of this text is familiar with the deinitions and concepts of pressure, temperature, enthalpy, entropy, heat and work (if not the reader is directed to Cengel & Boles 2007). However it is worth revising some of the important concepts of Classical hermodynamics. 2.1.1
System and Surroundings
In classical thermodynamics we are typically interested in changes in, and exchanges of, energy and mass between certain bodies (e.g. a tank of water or quantity of gas etc.). To clarify discussions, we call the particular body of interest (or region of space) the system. he system is oten (but not by necessity) contained within some physical boundary. Where the boundary of the system is such that matter (mass) is allowed to enter or leave the system, it is said to be an open system. Where the boundary of the system is such that mass is not allowed to enter or leave the system, but work and/or heat are allowed to be transferred across the boundary, the system is said to be a closed system. In the unusual case that the boundary of the system is such that neither mass nor energy (in the form of heat or work) is allowed to cross the boundary, the system is said to be an isolated system. he distinction between open and closed systems is important since thermodynamic analyses of closed systems tend to be simpler, by virtue of the fact that we do not have to consider the changes in energy of a system brought about simply by the transfer of mass with its intrinsic energy into or out of the system. his is the case with the refrigerant in a refrigerator or heat pump (provided there are no leaks), and hence we only need to consider work and heat transfer efects. Everything outside the system is known as the surroundings. here can be more than one system but typically we only talk about one ‘surroundings’. Note that the surroundings of a system of interest may simply be one or more other system(s) in their own right. Typically we are interested in transfers between the system and its surroundings. he system and surroundings combined make up what is referred to as the universe (this latter deinition is important when considering entropy changes). 2.1.2
Equilibrium
In classical thermodynamics equilibrium is a vital concept, because changes are expressed in terms of an initial state and a inal state, but changes are not considered with respect to time. (i.e. there is no concern for rates of change with respect to time). In order for a system to be at equilibrium, all forces (or, more generally, drivers of change) acting on it need to be balanced such that there is no net change to any of the system’s state variables with time.
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Refrigeration: Theory And Applications
2.1.3
Thermodynamics
State variables and path-dependent variables
Another important concept in classical thermodynamics is the concept of a state variable. To illustrate this concept, consider climbing the hill, as depicted in Figure 2.1. ůŝŵďŝŶŐĚŝƐƚĂŶĐĞʹ ƉĂƚŚĚĞƉĞŶĚĞŶƚ ǀĂƌŝĂďůĞ
ůƚŝƚƵĚĞʹ ƐƚĂƚĞǀĂƌŝĂďůĞ
Figure 2.1: Illustration of the diference between state and path dependent variables
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Thermodynamics
here may be a number of diferent trails you could follow to climb the hill, which will afect the distance that you travel; however, regardless of which path you take, your change in altitude (vertical displacement) depends only on your initial and inal altitudes. In this example, the distance travelled is a path-dependent variable, whereas altitude is a state variable. In thermodynamics examples of path-dependent variables include heat and work, while examples of state variables include temperature, pressure, speciic enthalpy, and speciic entropy. he name ‘state’ refers to the fact that state variables characterise or describe the physical state (i.e. condition) of the system. 2.1.4
Gibbs Phase Rule
You should be familiar with Gibb’s Phase Rule which allows us to determine the number of independent, intensive variables that need to be known in order for the system’s state to be speciied completely:
F =C−N +2
(2.1)
Where: F is the number of degrees of freedom (i.e. the number of variables that need to be speciied), C is the number of chemical components in the system and N is the number of phases in the system. Many common refrigerants are essentially pure chemical species (i.e. C = 1). If phase change is occurring then two phases are in equilibrium with each other (i.e. N = 2) and hence F = 1. hat is, when two species are in equilibrium (e.g. a liquid and vapour) there is only one degree of freedom, which means that if we specify one intensive state variable (e.g. temperature), then all the other intensive state variables (e.g. pressure, speciic enthalpy, speciic entropy) are ixed. If, however, only the liquid or vapour phases are present in the system, then we have N = 1 and F = 2, and hence we need to specify two intensive state variables before all the others are ixed. his information will be useful when we analyse the performance of diferent refrigeration cycles later in the chapter. 2.1.5
Reversibility and Irreversibility
Reversibility is yet another important concept in thermodynamics. In order for a process to be thermodynamically reversible, the following criteria must be met: 1. he system must be only ininitesimally removed from equilibrium at any stage of the process 2. he process must be able to be reversed at any stage of the process without leaving any impact on the surroundings (note that this second criterion is implied by the irst) hermodynamic reversibility is more speciic than simply referring to a process for with the opposite (or reverse) process is possible. Let’s illustrate from an every-day example. Consider the vertical window as depicted in Figure 2.2.
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Refrigeration: Theory And Applications
Thermodynamics
Figure 2.2: Closing a vertical window – irreversibly
he window is originally in its fully open position, held in place by the latch. If the latch is turned, releasing the window, it will lower itself spontaneously (probably with quite a crash!). We do not need to expend any energy in closing the window (other than turning the latch); however, we will need to do quite a lot of work to open the window (i.e. to return it to its original state). Now consider the vertical window depicted in Figure 2.3. his time there are counterweights for the window. If it is originally in its fully open position, when we turn the latch nothing will happen; the window will not close itself spontaneously. In order for the window to be closed we will need to apply a small downward force (to overcome friction). We can halt the process halfway, and leave the window half open. We can return the window to its original position simply be applying a small upward force. When the window is fully closed, returning it to its fully open position requires much less work than the window without counterweights.
Figure 2.2: Closing (or opening) a vertical window – reversibly
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Refrigeration: Theory And Applications
Thermodynamics
he window example illustrates that reversible processes are not spontaneous and therefore spontaneous processes are necessarily irreversible. Although we do not provide the proof here, thermodynamically reversible processes are the most energy eicient processes possible (returning to the window illustration – in principle we could open the counter-weighted window with a little inger, whereas the un-weighted window would require both hands with a signiicant force). True thermodynamic reversibility cannot be attained by any real-life processes due to friction and similar factors; however, a number of real life processes approximate reversibility. Examples include equilibrium chemical reactions, isothermal heat transfer (e.g. involving phase change), and some compression processes (think of a compressing or expanding a gas by adding or removing a grain to/from a pile of sand used as the weight for the piston doing the compressing).
2.2
The First Law of Thermodynamics
You should be familiar with the famous First Law of thermodynamics, which states that energy is not created or destroyed by any process; rather its form is changed. Of practical value to engineers and scientists is the mathematical expression of this statement, shown below for a closed system at rest:
DU = Q + W
(2.2)
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Refrigeration: Theory And Applications
Thermodynamics
(Note that the signs of Q and W in Eq. (2.2) depend on convention, but the important point to bear in mind is that work done on the system and heat transferred to it will increase U, and vice versa for work done by the system and heat transferred from it). Most refrigeration and heat pump processes operate in a cyclic manner, periodically returning the refrigerant to a given state. We can, therefore, say that over the cycle the net change in internal energy is zero, i.e.:
∫ DU = 0
(2.3)
cycle
and therefore the irst law for a closed, cyclic process can be written:
Qnet = Wnet
(2.4)
In refrigeration and heat pump cycles work is only performed during one stage of the cycle, while heat is transferred during two stages, one at a low temperature and one at a high temperature (the temperatures are ‘high’ and ‘low’ relative to each other, rather than in absolute terms). Hence the form of the First Law that will be most useful for analysing refrigeration or heat pump cycles is:
W = QH − QC
(2.5)
where W is work done on the refrigerant, and the subscripts H and C refer to the hot (high) and cold (low) temperature heat transfer processes respectively.
2.3
The Second Law of Thermodynamics
2.3.1
Statements of the Second Law
he Second Law of hermodynamics is perhaps slightly more abstract and harder to grasp than the First Law. To paraphrase Rudolf Clausius (1822 to 1888), the Second Law states that: It is impossible to construct a device operating in cyclic fashion whose sole purpose is to transfer heat from a low temperature reservoir to a higher temperature reservoir. At face value this statement might appear to suggest that refrigeration (which is a process having the net efect of transferring heat from a low temperature to a higher temperature) is a physical impossibility – more on this point later.
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Refrigeration: Theory And Applications
Thermodynamics
To get a mathematical expression of the Second Law, irst we need to recall the deinition of entropy (as used in classical thermodynamics) courtesy of Clausius:
DS = ∫
Qrev T
(2.6)
Mathematically, the Second Law can be written as:
DSuniverse = DS system − DS surroundings ≥ 0
(2.7)
We can state Eq. (2.7) verbally by saying that for any process the entropy of the universe can only increase, or in the limiting case (reversible processes) can remain unchanged. he Second Law states that the entropy of the universe can never decrease. So how do we reconcile Eq. (2.7) with Claudius’s statement? To answer this question, refer to Figure 2.4:
7+
4 7&
Figure 2.4: Heat low between hot and cold reservoirs
A quantity of heat Q is transferred between the thermal reservoir at temperature TH and another thermal reservoir at temperature TC where TH > TC (Note that a thermal reservoir is a large thermal mass at an essentially uniform temperature such that adding or removing quantities of heat will have a negligible impact on the reservoir’s temperature. Examples of thermal reservoirs include the atmosphere or large bodies of water such as lakes and seas). If the heat is transferred from the high temperature reservoir to the low temperature reservoir, the entropy change for the high temperature reservoir (DSH) is given by:
DS H =
−Q TH
(2.9)
And similarly for the low temperature reservoir
DSC =
Q TC
he total entropy change is therefore:
DS universe = DS H + DS C =
(2.10)
−Q Q + TH TC
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(2.11)
Refrigeration: Theory And Applications
Thermodynamics
Since TH > TC, DSH < DSC , and DSuniverse will be greater than 0, and therefore this process is allowable according to Eq. 2.7. By contrast, the reverse process is not permissible, which is where we get the statement that “heat only lows from hot to cold”, and demonstrates that Clausius’s statement of the Second Law is a necessary consequence of Eq. (2.7). So then how can refrigeration be possible, if heat cannot low from cold to hot? he answer is because the temperature of a body of mass can be raised or lowered without the transfer of heat, and this is how refrigeration works. here are a number of ways in which this can be achieved (and some of these will be discussed in Chapter 5); however, the vast majority of refrigeration and heat pump cycles in use today achieve the increase of temperature of the refrigerant by compressing it and the reduction of its temperature by expanding it adiabatically (thanks to the Joule-homson efect). 2.3.2
The Reversed Carnot Cycle and the COP
One of the key theories in the elucidation of the Second Law, was the Carnot Cycle. he Carnot Cycle is an ideal heat engine which operates according to four reversible processes: adiabatic expansion, isothermal compression, adiabatic compression, and isothermal expansion. During the irst process work is produced by the system, during the second heat is absorbed by the system, during the third work is done on the system, and during the fourth heat is rejected by the system.
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Since the cycle involves only reversible processes, any Carnot engine should be able to be operated in reverse as a heat pump or refrigerator, in which case the four processes would be adiabatic expansion, isothermal expansion, adiabatic compression and isothermal compression. he reversed Carnot cycle is illustrated on a temperature versus entropy (TS) plot shown in Figure 2.5:
Figure 2.5: Reversed Carnot cycle on a temperature-entropy (T-S) plot;
he heat rejected by the system during the isothermal compression can be calculated by a rearrangement of Eq. (2.6):
QH = TH DS
(2.12)
And during the isothermal expansion the heat absorbed is:
QC = TC DS
(2.13)
he net work input to the system is given by the First Law (Eq. 2.5):
W = QH − QC
(2.14)
Note that the work required to drive the reversed Carnot cycle is equal to the area enclosed by the cycle (the darker shaded area in Fig. 2.5). Combining Eqs. (2.12) to (2.14):
W = DS (TH − TC )
(2.15)
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Refrigeration: Theory And Applications
Thermodynamics
In order to assess the performance of the reversed Carnot cycle we introduce the coeicient of performance (COP). For a refrigerator, where we are interested in removing heat at a low temperature the COP is deined as:
COPR =
QC W
(2.16)
For a heat pump, where we are interested in the heat produced at the high temperature:
&23+3
4+ :
(2.17)
(he COP is essentially the eiciency of the refrigeration or heat pump cycle; however, because ‘eiciencies’ are generally deined such that they have values between 0 and 1, and COP values are usually greater than 1, traditionally the more cumbersome term COP has been used to keep the purists happy). Note that by substituting Eqs. (2.13 and 2.15 into Eq. 2.16) we can obtain simple expressions for the COPs of reversed Carnot cycles:
COPR =
&23+3
QC TC DS TC = = (TH − TC )DS TH − TC W
7+ :
7+ '6 7+ 7& '6
7+ 7+ 7&
(2.18)
(2.19)
Because the reversed Carnot cycle only employs reversible processes, it is the most eicient cycle possible (i.e. has the highest COP). herefore the COPs calculated for Carnot cycle provide benchmarks for real refrigeration and heat pump cycles to be compared against. By examining Eqs. (2.18) and (2.19) we see that the performance of the cycle is increased as we increase the target temperature (TC for a refrigerator, TH for a heat pump) and as we decrease the diference between the high and low temperatures. While these conclusions were derived for the idealised Carnot cycle, the conclusion is generally applicable for real refrigeration and heat pump cycles. It is also worth noting that:
&23+3
7+ 7+ 7&
7+ 7& 7& 7+ 7& 7+ 7& 7+ 7& 7 7& 7& + 7+ 7& 7+ 7&
&235
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(2.20)
Refrigeration: Theory And Applications
Thermodynamics
Or, more generally:
4+ : : 4& : &235
&23+3
(2.21)
Hence a device (e.g. the invertible domestic heat pump described in Chapter 8) will perform better as a heat pump than as a refrigerator, when operating between any two given temperatures. he reason for this is that the ‘waste product’ of the compression process is heat (essentially equal to W), which is included in QH, but not in QC.
2.4
Phase diagrams and refrigerant properties
he reversed Carnot cycle involves adiabatic and isothermal compressions and expansions. Obviously there needs to be some substance that is expanded or compressed, and this substance is known as the working luid, or, in the case of refrigeration speciically, the refrigerant. he desirable attributes of a refrigerant will be discussed in Chapter 4.
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State variables are physical attributes of a substance, and since we can relate thermodynamic processes (including refrigeration and heat pump cycles) to changes in state variables, we need to have access to the thermodynamic data of the refrigerant in order to select an appropriate refrigerant for a given task, and to perform preliminary calculations. he Gibbs Phase Rule tells us that if we have a pure substance we need to specify at most 2 state variables, in order for the remaining variables to be ixed. However, simply knowing the number of variables that need to be speciied does not tell us what the mathematical dependencies of the remaining state variables are. hankfully a lot of work has been performed over the years to measure, correlate and model these dependencies for a large number of working luids. he data may then be tabulated or plotted on a chart (or, these days, entered into an electronic database). A variety of sources may be consulted for the data including the ASHRAE Handbook of Refrigeration*, and the National Institute of Standards and Technology’s internet website (http://webbook.nist.gov). hermodynamic property charts are oten referred to as phase diagrams, because, typically the plots cover data over a number of diferent phases. In plotting a phase diagram, the choice of which variable to set on the abscissa (‘x-axis’) and which to set on the ordinate (‘y-axis’) will depend on its purpose. In the previous section the Carnot cycle was plotted on a TS or temperature entropy diagram, which was convenient because the Carnot Cycle involves isothermal and isentropic (i.e. the adiabatic compression and expansion) processes, and hence only lines parallel to an axis were required. Oten the properties of water are plotted as HS (enthalpy vs. entropy) diagrams called Mollier diagrams. However, the most common plot for refrigerants is the PH (pressure vs. enthalpy) diagram, an example of which is shown in Fig. 2.6 for the refrigerant R-134a , whose chemical name is 1,1,1,2-tetraluoroethane (if you are curious about the naming convention for refrigerants, refer to the ASHRAE Handbook of Refrigeration). 10
T = 80 °C
T = 60 °C
T = 40 °C
T = 20 °C
1 T = 0 °C
P (Mpa)
T = -20 °C T = -40 °C
0.1 T = -60 °C T = 80 °C
T = 40 °C
T = 0 °C
0.01 0
100
200
300
400
h (kJ/kg)
Figure 2.6: Pressure-enthalpy diagram for Refrigerants R-134a
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500
600
Refrigeration: Theory And Applications
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(Note that a slightly larger version of this chart may be found in the Appendix – Figure A.1)
In Fig. 2.6, the blue line corresponds to the saturated liquid, the red line corresponds to the saturated vapour, the green lines correspond to isotherms (note the sharp change in the gradient of isotherms as they enter and exit the two-phase region) and the black lines correspond to lines of constant entropy (‘isentropes’). he point where the saturated liquid and vapour lines meet is known as the critical point. Above the critical temperature and critical pressure of the luid the distinction between liquid and gas is vague with density gradients rather than a sharply deined interface between phases, and the luid is said to be supercritical. Most PH diagrams include more isotherms and isentropes than are shown in Fig. 2.6, and also include lines of constant speciic volume (the inverse of density). However, the more data included in the chart, the harder they are to read, so Fig. 2.6, is drawn speciically to contain suicient data to perform the worked examples in this chapter. A larger version of Fig. 2.6 is provided in the Appendix (Figure A.1). PH diagrams are useful for obtaining a visual representation of a refrigeration or heat pump cycle; however, since the precision of the data is limited by the size of the chart and the amount of data it contains, only the most basic calculations can be performed. For greater accuracy, tabulated data are more practical to use. he Appendix includes tabulated data for saturated R-134a and superheated R-134a (we do not oten need to worry about sub-cooled liquid data, since in refrigeration cycles we do not tend to operate far away from saturation in the liquid phase). Example 2.1: Use Fig. 2.6 the diagram to determine the enthalpy of saturated liquid R134a at 1 bar. Solution: 1 bar = 105 Pa = 0.1 MPa. We locate 0.1 MPa on the pressure axis of Fig. 2.6 and then follow the line across to the intersection with the blue saturated liquid line, then read horizontally downward to the enthalpy axis, which yields an enthalpy of approximately 165 kJ kg-1. Note: Temperatures and pressures involved in plotting Fig. 2.6 are absolute; however, the data for enthalpy and entropy depend on the speciication of a reference state, and hence diferent sources will give diferent values of the enthalpy of the saturated liquid R-134a at 1 bar. However, regardless of the source, any enthalpy diference determined from a PH diagram for a particular refrigerant should have a single result. he data in Fig. 2.6 and Table A1 were obtained from the same source, so all numbers including the enthalpy and entropy data will be the same. Example 2.2: Use the data in Table A2 (Appendix) to determine the enthalpy of superheated refrigerant R-134a if the temperature is 100 °C and the entropy is 1.95 kJ kg-1 K-1.
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Solution: Find 100 °C in the temperature column in Table A2 and then read horizontally across until you come to the entry closest to 1.95 kJ kg-1 K-1, which occurs in the P = 0.6 MPa section of the table. hen read the enthalpy value in the neighbouring column, i.e. 487.6 kJ kg-1. Example 2.3: Calculate the enthalpy diference between saturated liquid R134a at 40 °C and superheated R134a at 0.5 MPa and the same temperature. Solution: his problem can be solved either by using Fig. 2.6 or by using Tables A1 and A2. However, since the point on the saturation curve has been speciied in terms of its temperature, less interpolation or rounding will be required using the tables, since the independent variable in Table A1 is temperature (if the saturated liquid pressure was supplied then Fig. 2.6 might have been simpler to use). Let h1 refer to the speciic enthalpy of the saturated liquid and h2 refer to the enthalpy of the superheated vapour. From the ‘hf’ column in Table A1 at 40 °C, h1 = 256.4 kJ kg-1; from Table A2 at 40 °C and 0.5 MPa h2 = 430.6 kJ kg-1. he diference is: Δh = h2 – h1 = 430.6 – 256.4 = 174.2 kJ kg-1.
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2.5
Thermodynamics
Vapour Compression Cycles
Can we implement the reversed Carnot cycle in real life? here are, in fact, a number of hurdles that so far have prevented anyone from developing a genuine, practical Carnot refrigerator or heat pump. First of all, in order to achieve the isothermal processes, we would like to operate the cycle within the twophase region of the refrigerant (i.e. under the saturation curves in Fig. 2.6) so that heat exchange causes phase-change rather than change in sensible heat. However, it is very diicult to manufacture turbines and particularly compressors that will cope with two-phase lows. If we operate in a single-phase region (most likely the gaseous region), our expansion and compression processes can, in principle approach reversibility, with practical mechanical designs; however, it is diicult to achieve the isothermal processes. So where should we make the compromise? 2.5.1
Ideal vapour compression cycles
he most commonly used refrigeration cycle is known as the vapour-compression cycle, and accounts for roughly 95% of the world’s mechanical refrigerators and heat pumps. he ideal vapour compression cycle is illustrated in Fig. 2.7 on TS and PH diagrams, along with a schematic of the hardware. It consists of four processes: isentropic vapour compression, isobaric sub-cooling and condensation, isenthalpic liquid expansion, and isothermal (and isobaric) evaporation. As much as possible, the heat transfer processes occur within the two-phase region, in order to beneit from the eiciency of isothermal processes. Unlike the reversed Carnot cycle, however, the compression process occurs outside the two-phase region which causes the temperature of the refrigerant to rise signiicantly above the condensation temperature. his is done to avoid two-phase low that would damage the compressor. he other key diference between the ideal vapour compression cycle and the reversed Carnot cycle is that we do not attempt to recover work during the expansion process, and simply throttle the refrigerant adiabatically. However, the adiabatic throttling causes some of the refrigerant to evaporate, reducing the quantity of heat that can be absorbed. 10
10
T
P 2 3
1
2
3
1
4
1
1
4 0.1
0.1
0.01
0.01
0.5
1
1.5
2
0
s
a)
100
200
b)
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400
500 h
Refrigeration: Theory And Applications
Thermodynamics
QH
3
2
Condenser
W
Valve
4
Evaporator
Compressor
1
QC c) Figure 2.7: Ideal vapour-compression cycle: a) T-S diagram, b) P-H diagram, c) schematic
In practical refrigerators, PH diagrams are generally preferred to TS diagrams for plotting the cycle. By plotting an ideal-vapour compression cycle on a PH diagram we can perform relatively straightforward estimates of work, heat and COPs of the cycle. he work (W) required to drive the cycle is equal to the enthalpy change of the refrigerant during the compression process, i.e. the work is equal to the enthalpy change between points 1 and 2 in Fig. 2.8. he heat absorbed by the refrigerant in the evaporator is equal to the diference in enthalpy between points 1 and 4 and the heat rejected (QH) by the refrigerant in the condenser is equal to the diference in enthalpy between points 2 and 3. Once we know W, QC and QH we are able to calculate COPR and COPHP using Eq. 2.16 or Eq. 2.17. Example 2.4: Consider the ideal vapour compression cycle using R-134a as the refrigerant, and operating with a condenser temperature of 40 °C of and an evaporator temperature of –20 °C, as shown in Fig. 2.8. Calculate the amount of cooling (QC) and the work (W) input required.
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10 T = 80 °C
T = 60 °C
T = 40 °C
T = 20 °C
1
3
2
T = 0 °C
P (Mpa)
T = -20 °C T = -40 °C
4
0.1
1
T = -60 °C T = 40 °C
430
T = 80 °C
T = 0 °C
385 400
0.01 0
100
200
255
300
500
600
h (kJ/kg)
Figure 2.8: Refrigeration cycle based on R-134a for Examples 2.4 and 2.5
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Solution: he amount of heat removed is equal to the diference in enthalpy of the refrigerant between the inlet and the outlet of the evaporator, i.e. the diference in enthalpy between State 1 and State 4. he speciic enthalpy at State 1 can be obtained from Figure 2.8 by reading the ‘x-coordinate’ of point 1, i.e. h1 = 385 kJ kg-1. Likewise h4 = 255 kJ kg-1. Hence: QC = h1 – h4 = 385 – 255 = 130 kJ kg-1 Similarly, the amount of work required is equal to the diference in enthalpy between the inlet and the outlet of the compressor, i.e.: W = h2 – h1 = 430 – 385 = 45 kJ kg-1 Once we know QC and W, we can determine QH by using the First Law: QH = QC + W = 130 + 45 = 175 kJ kg-1 Alternatively we could have read it from the chart: QH = h2 – h4 = 430 – 255 = 175 kJ kg-1 Example 2.5: For the cycle depicted in Fig. 2.8 calculate COPR and the mass low-rate of refrigerant that would be required to achieve 2 kW of cooling. Solution: he COPR can be determined easily using Eq. 2.16 and the results from Example 2.4:
&235
4& :
K K K K
In order to calculate the mass low-rate of refrigerant required we recognise that the enthalpy, heat and work data that we have been using so far have units of kJ kg-1. We want to know what mass low-rate will give us heat low with units of kW (i.e. kJ s-1). his should immediately suggest the following relationship:
§ NJ · § N- · § N- · : ¨ ¸ P ¨ ¸: ¨¨ ¸¸ © V ¹ © NJ ¹ © V ¹ : Rearranging, we can solve for m
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: :
P
NJV
Example 2.6: An ideal vapour compression cycle using R-134a operates with a suction pressure of 0.2 MPa and a discharge pressure of 1.0 MPa. Using the thermodynamic property tables for R134a in the Appendix calculate: a) the evaporator and condenser temperatures, b) the temperature at the compressor discharge, c) COPHP Solution: he ‘suction’ pressure refers to the pressure of the refrigerant at the inlet of the compressor, which corresponds to the pressure at States 1 and 4 in Fig. 2.7b. he ‘discharge’ pressure refers to the pressure of the refrigerant at the outlet of the compressor, which corresponds to the pressure at States 2 and 3. a) Since States 1 and 3 lie on the saturation line, there is only one degree of freedom, so if we know one state variable (pressure, in this case) we can use Table A1 to ind all the other state variables. Figure 2.7b shows that the State 1 is at the evaporator temperature, and State 3 is at the condenser temperature. From Table A1, the temperature of saturated R134a at 0.2 MPa (i.e. T1, the evaporator temperature) is -10 °C. he temperature of saturated R134a at 1.0 MPa (i.e. T3, the condenser temperature) is 40 °C. b) When the refrigerant exits the compressor it is in the superheated state (see Figures 2.7a and 2.7b), and therefore it has two degrees of freedom, and a variable in addition to the pressure needs to be speciied in order for the state to be completely deined. In the case of the ideal vapour-compression cycle, we have assumed perfect, isentropic compression, i.e. the entropy of the refrigerant at the compressor discharge is assumed to be the same as the entropy at the suction, hence s1 = s2 (this is shown in Figure 2.8 where the pathway between States 1 and 2 lies along an isentrope). Since State 1 is completely deined by specifying one state variable, we can determine s1 from Table A1 by inding the value in the ‘sg’ column which corresponds to P1 (i.e. 0.2 MPa), hence s2 = s1 = 1.73 kJ kg-1 K-1. To determine the temperature at State 2, we need to ind the temperature which corresponds to a pressure of 1.0 MPa and an entropy of 1.73 kJ kg-1K-1 in Table A2. Locating the columns under the ‘P = 1.0 MPa’ heading in Table A2 we see that when s = 1.73 kJ kg-1 K-1 the refrigerant temperature is 45 °C, i.e. T2 = 45 °C. c) To calculate COPHP, we observe that for an ideal vapour-compression cycle:
&23+3
4+ :
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K K K K
Refrigeration: Theory And Applications
Thermodynamics
Since States 1 and 3 lie on the saturation curve, we can read h1 from the saturated vapour column (hg) of Table A1 when P = 0.2 MPa, i.e. h1 = 392.7 kJ kg-1, and h3 from the saturated liquid column (hf) of Table A1 when P = 1.0 MPa, i.e. h3 = 256.4 kJ kg-1. In the solution to part b) of this problem we determined that s2 = 1.73 kJ kg-1 K-1 in addition to P2 being given as 1.0 MPa. herefore we can obtain h2 by locating the enthalpy value next to the s = 1.73 kJ kg-1 K-1 entry in the ‘P = 1.0 MPa’ heading of Table A2, i.e. h2 = 425.4 kJ kg-1. Hence:
&23+3
K K K K
Note: COPR can be calculated very simply from COPHP by apply Eq. 2.20:
&235 &23+3
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2.5.2
Thermodynamics
Practical vapour compression cycles
In the previous section we studied the ideal vapour compression cycle, in which the evaporation and condensation processes occurred isobarically, the compression occurred isentropically, and the expansion occurred adiabatically. In addition, it was assumed that the refrigerant was in the saturated vapour state when it entered the compressor, and in the saturated liquid state at the start of the expansion process. In real vapour-compression devices none of these assumptions is likely to be entirely accurate, and it is worth considering factors which prevent real vapour-compression devices from operating ideally. Non-isentropic compression process: only a truly reversible compression process is isentropic (i.e. 100% eicient). In practice the compression process has an eiciency which is usually greater than 80% of the truly isentropic process. Non-isobaric operation: the reader should also bear in mind that in refrigeration applications larger than the domestic setting, there may be a signiicant length of piping between the evaporator and the compressor, and the condenser and the expansion valve. Most systems also have a refrigerant ilter/dryer in the line to prevent solid particles or water droplets entering and damaging the compressor. Friction between the refrigerant and the tubing, ittings and manifolds which contain it, along with bends, expansions and restrictions all serve to reduce the pressure of the refrigerant as it passes through the system. Condition of the refrigerant entering the compressor: in practice, the risk of having liquid droplets in the compressor means that measures are taken to ensure that all the refrigerant has evaporated before it enters the compressor, which oten means that it is super-heated slightly. In practice this is oten achieved with the use of an accumulator, a simple device which uses gravity to separate vapour from any liquid. Condition of the refrigerant entering the expansion valve: although expansion valves are not damaged by two-phase low, it is diicult in practice to control the condensation process such that the refrigerant is a saturated liquid as it enters the expansion valve. Additionally, it is reasonably common practice to charge the system with an excess of refrigerant as a safety margin, to prevent poor performance or damage caused by too little refrigerant in the system (especially given that refrigerant may be lost from the system due to leakage). he excess refrigerant is usually stored in a device known as a receiver, which is commonly drum-shaped. For this reason, the refrigerant is usually sub-cooled when it enters the expansion valve. Adiabatic (isenthalpic) expansion process: a well-insulated valve should produce an expansion that is very close to being truly isenthalpic; however, if there is no insulation around the valve, the refrigerant will absorb heat before it enters the evaporator, thereby reducing the cooling capacity of the system. Figure 2.9 Shows a PH plot of a more realistic vapour compression cycle superimposed on the ideal vapour compression cycle shown in Figure 2.7b. he two cycles (realistic and ideal) have the same suction and discharge pressures. he following implications of the diferences in the realistic and ideal cycles may be observed:
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- he efects of the non-isentropic compression process are seen in the fact that compression pathway of the realistic cycle proceeds to the right of the pathway of the ideal compression process, and hence more work is required to achieve the same compression (i.e. h2 – h1 for the realistic process is greater than it is for the ideal process) - he non-isobaric nature of the passage of the refrigerant between the compressor and expansion valve mean that the average temperature in the condenser of the realistic system is lower than in the ideal system, and conversely the average temperature in the evaporator of the realistic system is higher than in the ideal system. his means that the compressor of the realistic system will need to have a higher compression ratio (i.e. will need to do more work) than the compressor in the ideal system to operate between the same load and ambient temperatures - A well-insulated expansion valve should, in principle, approximate isenthalpic expansion; however, a poorly insulated valve will result in a reduced COPR, since it reduces the amount of liquid refrigerant entering the evaporator, and hence reduces the enthalpy of vaporisation available for heat absorption. his can be seen in Figure 2.9a: the refrigerant passing through a well-insulated valve will follow the path from 3b to 4; whereas refrigerant passing through an un-insulated valve will follow the path from 3b to 4’. Clearly (h1a – h4) is greater than (h1a – h4’).
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QH 3a Receiver
2
Condenser
3b W
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1b Accumulator
Evaporator 1a
QC b)
Figure 2.9: a) Comparison of realistic (solid line) and ideal (dashed line) vapour compression cycles operating between the same suction and discharge pressures; b) schematic of realistic refrigeration apparatus with accumulator, receiver and ilter-dryer
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Example 2.7: A real vapour-compression refrigeration cycle operates with a suction pressure of 0.2 MPa and a compression ratio of 5. he refrigerant enters the compressor close to saturation and exits at 50 °C. At the start of the expansion process it is essentially saturated at 36 °C. Calculate: a) isentropic eiciency of the compression process, where the isentropic eiciency is deined (with reference to igure 2.9b) by:
η=
Wisentropic Wactual
=
hisentropic − h1b h2 − h1b
(2.22)
b) the COPR, assuming that the system is suiciently well-insulated that the only signiicant heat absorption occurs in the evaporator. c) the cooling capacity of the system under these conditions if the refrigerant low-rate is 0.05 kg s-1. Solution: for this exercise it is most convenient to use the refrigerant property tables A1 and A2; however, it may be helpful for the reader to refer to Figure 2.9 to identify which states and processes are being discussed. a) In order to calculate the isentropic eiciency using Eq. 2.22 we need to determine h1b, h2 and hisentropic. Since the information given is that the refrigerant enters the compressor essentially as a saturated gas (i.e. there is negligible diference between h1a and h1b) we can determine h1b from inding the enthalpy of the saturated vapour at 0.2 MPa from Table A1, which is 392.7 kJ kg-1 K-1. he compression ratio of 5 means that the outlet pressure is 1.0 MPa, and since the outlet temperature was given as 50 °C, we have the two state variables necessary for determining the state of the superheated refrigerant using Table A2, i.e. h2 = 430.9 kJ kg-1 K-1. hisentropic is the enthalpy of the refrigerant that would have resulted from an isentropic compression, and so we can determine its value by determining the entropy of the refrigerant at the inlet and using that entropy along with the exit pressure to determine hisentropic from Table A2 (the same as for the calculation of h2 in Example 2.6c), i.e. s1a = s1b = 1.73 kJ kg-1 K-1 (from Table A1 at 0.2 MPa), and therefore hisentropic = 425.4 kJ kg-1 (from Table A2 with s = 1.73 kJ kg-1 K-1 and P =1.0 MPa) Hence:
K
KLVHQWURSLF KE K KE
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b) We can calculate COPR in this example from:
COPR =
QC h − h4 = 1a Wactual h2 − h1b
Having determined h1a and h2 in part a), and given that there is negligible diference between h1a and h1b it remains for us to determine h4. Although State 4 lies within the saturation region, we cannot know its enthalpy simply from its temperature and/or pressure, without knowing what fraction of the refrigerant is in the liquid state, and what fraction is vapour. If we plotted the cycle accurately on a P-H or T-S diagram, we could use the Lever rule to estimate this fraction; however, since the problem states that the system is well insulated, it is reasonable to assume that the expansion occurs isenthalpically, and hence that h4 = h3b. h3b is the enthalpy of the refrigerant at the start of the expansion process, which was given as saturated liquid at 36 °C, so h3b = h4 = 250.5 kJ kg-1 K-1 (from Table A1). Hence:
COPR =
h1a − h4 392.7 − 250.5 = 3.7 = h2 − h1b 430.9 − 392.7
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c) Calculating the cooling capacity of this refrigeration system under these conditions is straight-forward:
4 &
4& P
KD K u N: P
Note: Example 2.7 was essentially the more realistic version of the ideal scenario of Example 2.6. In Example 2.6 and COPR,ideal was 4.2 and COPR,realistic calculated in Example 2.7 was 3.7, which illustrates the efect irreversibilities have on performance. However, it should be pointed out that had we calculated the COP based on the total power drawn by the system it would have been lower, since power is required to run the control system and typically fans on one or both of the heat exchangers.
2.6
Cascade and multi-stage vapour compression cycles
he performance of an ordinary vapour compression cycle can be improved in a number of ways, at the expense of extra capital costs. Eq. 2.23 shows the work required for an adiabatic (isentropic) compression process:
Z
J ª º 57 «§ 3 · J ¨¨ ¸¸ » « » J © 3 ¹ ¬« ¼»
(2.23)
Where R is the Universal Gas Constant, and γ is the ratio of speciic heat capacity at constant pressure to the speciic heat capacity at constant volume. Eq. 2.23 reveals that the work is required is directly proportional to the suction temperature (the temperature of the gas as it enters the compressor) and is also proportional to the compression ratio. Since the suction temperature will be set by the desired temperature in the evaporator, the single most efective way to reduce the work requirement for a given refrigeration load is to divide the compression process into stages with intercooling between stages. 2.6.1
Cascade refrigeration
Consider the ideal, single-stage vapour compression cycle shown by the dotted black line in Figure 2.10a (path 1→2'→7→4'). In this case the condensation and evaporation temperatures (and hence pressures) are relatively far apart and the liquid fraction of refrigerant which enters the evaporator is relatively low (hence the heat absorption potential is also relatively low). Now consider a modiication to the singlestage vapour compression cycle as shown schematically in Figure 2.10b. In this modiied refrigeration system, there are actually two cycles operating in two diferent pressure (and hence temperature) ranges.
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Condenser
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4
Compressor
1
QC b)
Figure 2.10: Cascade refrigeration system
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Refrigeration: Theory And Applications
Thermodynamics
he heat exchanger that connects the two cycles serves as the evaporator for the high pressure cycle (depicted by the solid blue line following the path 5→6→7→8) and the condenser for the low pressure cycle (depicted by the solid blue line following the path 1→2→3→4). he arrangement shown in Figure 2.10 is knows as a cascade of refrigeration cycles, or cascade refrigeration. he advantages of cascade refrigeration over a single-stage cycle is that there is greater cooling potential LH '4& K· ± K when operating between the same condensation and evaporation temperatures, and for a given cooling load the compression work will be lower. his means that the COP of cascade refrigerators will be higher than single-stage refrigerators operating between the same temperatures. he penalty of the improved performance, though, is in more equipment and hence higher capital costs. In addition to ofering greater eiciency than single-stage refrigeration, cascade refrigeration will be able to perform some refrigeration tasks that single-stage refrigeration cannot. If the diference between the condensation and evaporation temperatures is large the compression ratio required to operate between the two temperatures may be too large for practical compressors. Using cascade refrigeration, the overall compression can be broken up into manageable compression ratios.
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Note that refrigerant low-rates will not necessarily be the same for each vapour compression cycle within a cascade. In order for the cascade refrigerator to function properly, there must be an enthalpy balance over the heat exchanger between the two cycles. Referring to the notation in Figure 2.10, the enthalpy balance is given by:
m H (h5 − h8 ) = m C (h1 − h4 )
(2.24)
H refers to the mass low-rate of refrigerant in the top (higher temperature) cycle, and m C refers Were m to the mass low-rate in the bottom (lower temperature) cycle. he cycles in a cascade refrigerator, need not employ the same refrigerant, which means that diferent refrigerants can be selected for the diferent cycles, depending on which refrigerant has the optimal thermodynamic properties (i.e. the refrigerant with optimal thermodynamic properties in the higher temperature range may not be the optimal refrigerant in the lower temperature range). However, if the same refrigerant is used in all cycles, a modiication of cascade refrigeration known as multi-stage refrigeration, may work more eiciently. 2.6.2
Multi-stage refrigeration
Figure 2.11 shows an ideal multi-stage refrigeration cycle. he key diference between the multi-stage and cascade refrigeration cycles is the absence of the heat exchanger between separate vapour compression cycles. Instead, ater the refrigerant is dropped from the condenser pressure to the intermediate pressure (path 7→8 in Figure 2.11), the gaseous fraction is separated from the liquid fraction using a lash drum (or lash chamber). he liquid fraction is then expanded again before it passes through the evaporator, and then the Compressor 1 (path 3→4→1→2 in Figure 2.11). he vapour coming from Compressor 1 (which is in the superheated state) is then mixed with the saturated vapour coming from the lash drum (path 8→9 in Figure 2.11), and the mixture is then compressed from the intermediate pressure to
the higher pressure before it passes through the condenser, and the cycle is completed (path 5→6 →7). Clearly this arrangement will only work if the same refrigerant is used throughout the cycle, and so it will not necessarily be more eicient than an optimised cascade refrigerator.
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Refrigeration: Theory And Applications
Thermodynamics
ϭϬ
3
ϭ
Ϭ͘ϭ
Ϭϭ Ϭ
ϭϬϬ
ϮϬϬ
ϯϬϬ
ϰϬϬ
ϲϬϬ K
ϱϬϬ
a)
QH
6
7
Condenser
W
Valve 2
Compressor 2
5
8 Flash drum
9
2
Mixer
3 W
Valve 1
Evaporator
4
Compressor 1
1
QC b)
Figure 2.11: Multi-stage refrigeration system
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Thermodynamics
Example 2.8: Compare the COPR values of a single-stage ideal vapour compression cycle with a two-stage, ideal cascade refrigerator both using R134a with a cooling load of 6 kW at an evaporator temperature of -26 °C. he condenser pressure is 1.0 MPa, and for the sake of simplicity, you may assume that the evaporation and condensation processes in the heat exchanger both occur at a constant pressure of 0.3 MPa (although this would require ininite heat exchange area in reality). PH diagrams of the two systems are shown in Figure 2.12. 10
10
P
P 3s
6c
7c
2s 1
1
3c
1s
4s
0.1
5c
8c
1c
4c
0.1
2c
0.01
0.01 0
100
200
300
400
500
600 h
0
100
200
300
400
500
600 h
Figure 2.12: P-H diagrams for the single-stage and cascade refrigeration systems in Example 2.8
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Thermodynamics
Solution: he COPR of the single-stage vapour compression process can be determined using the same steps as were used in Example 2.6. Using the information provided and Tables A1 and A2 (note that the subscript ‘s’ refers to the single stage cycle, while the subscript ‘c’ refers to the cascade cycles): P1s = 0.1 MPa, h1s = 383 kJ kg-1, s1s =1.75 kJ kg-1 K-1
(Table A1)
P3s = 1.0 MPa, h3s = 256 kJ kg-1 = h4s
(Table A1)
P2s = 1.0 MPa, s2s = s1s = 1.75 kJ kg-1 K-1, h2s = 430 kJ kg-1
(Table A2)
COPR , s =
h1 − h4 383 − 256 = 2.7 = h2 − h1 430 − 383
We can calculate the mass low-rate of refrigerant required as follows:
V P
4 & 4&
4 & K K
NJV
N: N-NJ
For the cascade system: P1c = P1s = 0.1 MPa, h1c = h1s = 383 kJ kg-1, s1c = s1s = 1.75 kJ kg-1 K-1
(Table A1)
P3c = 0.3 MPa, h3c = 200 kJ kg-1 = h4c
(Table A1)
P2c = 0.3 MPa, s2c = s1c = 1.75 kJ kg-1 K-1, h2c = 405 kJ kg-1
(Table A2)
P5c = 0.3 MPa, h5c = 399 kJ kg-1, s5c = 1.73 kJ kg-1 K-1
(Table A1)
P7c = 1.0 MPa, h7c = 256 kJ kg-1 = h8c
(Table A1)
P6c = 1.0 MPa, s6c = s5c = 1.73 kJ kg-1 K-1, h2c = 425 kJ kg-1
(Table A2)
To calculate the COPR of the cascade refrigerator, we will need to calculate low-rates of refrigerant in the two loops as follows:
m C
Q C QC
m H
m C
Q C h1c h4c
(h2c (h5c
h3c ) h8c )
6 383 200
0.0328
0.0328 kg s
405 200 399 256
1
0.0470 kg s
1
The combined work input to the compressors in the cascade system is given by:
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Refrigeration: Theory And Applications
Thermodynamics
he combined work input to the compressors in the cascade system is given by:
:F
:& : +
& KF KF P + KF KF P
u u N:
Hence:
&235 F
4& :F
Note: he cascade refrigeration system requires less work for the same cooling load, but has a greater charge of refrigerant and requires more plant (i.e. extra compressor, heat exchanger and valve plus auxiliaries).
2.7
Sorption refrigeration
So far we have considered vapour compression cycles which make up the vast majority of commercial refrigeration, heat pump and air conditioning units. However there is a wide range of practical alternatives to vapour compression as a means of transferring heat from a low temperature to a high temperature. Many of these, such as the thermo-electric devices, magnetic refrigeration and acoustic refrigeration are currently limited to small-scale and niche applications, and these will be covered briely in Chapter 5. Probably the only rival to vapour-compression on the medium to large scale is sorption refrigeration, a collective term for absorption and adsorption refrigeration. Sorption refrigeration cycles are similar in principle to vapour compression cycles, with the main diference being that vapour compression is replaced in a novel way such that the work input required to drive the cycle is very small, and instead the cycle is essentially driven by heat. Consider the schematic of the absorption refrigeration cycle shown in Figure 2.13. Comparison of Figure 2.13 with Figure 2.7c illustrates that the condenser, expansion valve and evaporator are the same for both cycles. he diference occurs once the refrigerant vapour leaves the evaporator, where, in the case of absorption refrigeration, instead of entering a compressor it is dissolved in a liquid absorbent. he refrigerant/absorbent mixture is then pumped to the condenser pressure where the refrigerant vapour is liberated in the generator by heat from an external source such as industrial waste heat or solar energy.
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Thermodynamics
QH
Condenser
Qreg
Rectifier
Regenerator
Valve
Heat Exchanger
Absorber
Evaporator
QCoolant
QC
Pump
W
Figure 2.13: Schematic of an absorption refrigerator
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Thermodynamics
he vapour stream from the regenerator is comprised mainly of refrigerant; however, it will most likely contain some entrained absorbent as well. he remaining absorbent is separated from the refrigerant in the rectiier, and then returned to the regenerator, while the refrigerant vapour enters the condenser and the cycle is repeated. he liquid phase in the regenerator which is mainly made up of absorbent, but will most likely contain a small amount of un-liberated refrigerant is returned to the absorber. Since the liquid stream entering the absorber needs to be heated, and the liquid stream leaving the regenerator needs to be cooled, they are passed through a heat exchanger, which reduces the external heating and cooling duties. Generally speaking, the lower the temperature of the absorbent, the more refrigerant it will be able to dissolve, so there is an incentive to actively cool it, at least with cooling water (i.e. water at ambient temperature). Clearly the interaction between the refrigerant and absorbent plays a key role in their selection. he refrigerant needs to be highly soluble in the absorbent at low temperature and pressure and only sparingly soluble at higher temperature and pressure. A common pairing is ammonia as the refrigerant and water as the absorbent. Ammonia, which is an excellent refrigerant in a vapour compression cycle, is highly soluble in water at low temperatures, but also has a much higher vapour pressure than water, so is easily liberated at higher temperature. he disadvantage of ammonia is that it is highly lammable and toxic, which means that it is best suited to industrial applications were proper maintenance and safety precautions are likely to be practiced. Another common pairing is water as the refrigerant and an aqueous solution of lithium bromide as the absorbent, although this system is limited by the relatively high freezing temperature of water, and the hazardous nature of lithium bromide. A COP is essentially the ratio of the cooling output to the energy input. For a sorption refrigerator this means:
COPR , Abs =
Qreg
QC Q ≈ C + W + Qcool Qreg
Sorption refrigerators are more complex and require greater maintenance than vapour-compression refrigerators, and are signiicantly less eicient. heir advantage, however, is that under the right circumstances they are cheaper to run. Liquid pumping is far less energy intensive than vapour compression, and in terms of the absorption refrigerator, the work input is almost negligible. If the heat input comes from a solar thermal array or industrial waste heat then it is essentially ‘cost-free’ energy, in which case the lower eiciency of the system can easily be justiied economically.
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Since the work required to run the cycle is small, and the heat source is likely to be renewable (solar) or ‘recycled’ (waste heat), another factor in the absorption refrigerator’s favour is that it can be argued that it has less impact on the environment, especially in countries where electricity is generated by nonrenewable methods.
2.8
Summary of Chapter 2
he majority of refrigerators, air conditioners and heat pumps operate using the vapour compression cycle. he performance of these devices is measured by the ratio of the amount of cooling (in the case of refrigerators and air conditioners) or heating (in the case of heat pumps) delivered divided by the work required to run the cycle, which is mainly associated with the compression stage. his ratio is known as the coeicient of performance, or COP:
&235
4& &23+3 :
4+ :
he most eicient refrigerator or heat pump possible operates using the reversed Carnot cycle, and it was shown that the COPs for a reversed Carnot cycle are:
&235 &DUQRW
7& &23+3 FDUQRW 7+ 7&
7+ 7+ 7&
he COPs of the reversed Carnot cycle illustrate principles that are generally true of real devices: - he performance of refrigerators and heat pumps is increased by an increase in the target temperature (TH or TC), and decreased by an increase in the diference between TH and TC - Any device that may be operated both as a heat pump and a refrigerator (e.g. the typical domestic heat pump) will have a higher COP when operated as a heat pump than as a refrigerator For set values of TH and TC, the COPs for devices employing the vapour compression cycles may be increased by breaking the overall compression process into stages, by employing cascade or multi-stage refrigeration. Sorption refrigeration ofers the main alternative to vapour compression refrigeration, and can be thought of as being driven by heat rather than by work. Sorption refrigerators are generally less eicient than vapour compression refrigerators, but they can be cheaper to run and have the potential to have less impact on the environment.
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Refrigeration: Theory And Applications
2.9
Thermodynamics
Further Reading
ASHRAE Handbook: Refrigeration, American Society of Heating, Refrigeration and Air Conditioning Engineers, Atlanta, GA, 2010 Çengel, YA & Boles, MA, hermodynamics: An Engineering Approach, 7th Ed., McGraw Hill, New York, 2011 Smith, JM, van Ness, HC & Abbott, MM., Introduction to Chemical Engineering hermodynamics, 7th Ed., McGraw Hill, New York, 2005 Whitman, WC, Johnson, WM, Tomczyk, JA & Silberstein, E, Refrigeration and Air Conditioning Technology, 6th Ed., Delmar, New York, 2009
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3 Heat Transfer Classical thermodynamics considers changes between thermodynamic states (i.e. changes in variables such as temperature, pressure, enthalpy etc.) but not the rate at which changes occur. However, rates of change are oten important for practical purposes. High eiciency designs or processes, as identiied by the Laws of hermodynamics, may be too slow to be practical, and some compromise between energy eiciency and practicality will oten be required. For this reason we need a separate, but related discipline known as ‘heat transfer’ (also known as ‘heat transport’ or ‘heat transmission’), which is the science concerned with calculating heat lows and temperatures as a function of time and location.
3.1
Modes of heat transfer
Heat may be transferred by three diferent mechanisms: - Conduction is the transfer of thermal energy from high-temperature regions of a substance to adjacent, lower-temperature regions as a result of physical interaction between atoms/ molecules in the form of collisions and vibrations. - Convection is the combined efect of conduction and luid motion, from density diferences (buoyancy), wind or natural water lows, or mechanical means - hermal Radiation is energy emitted by matter in the form of electromagnetic waves (or photons) over a range of wavelengths. It does not occur as the result of direct physical contact between atoms or molecules. As a generalisation, we are concerned with conduction within solids, and convection within luids and radiation between surfaces separated by a luid. Radiation is the most diicult of the three modes to model mathematically and in refrigeration applications its inluence is relatively minor (although certainly not negligible) and hence its efects may oten be approximated simply or combined with the efects of convection, as will be assumed to be the case throughout the remainder of this chapter.
3.2
Steady state conduction and convection
Many of the heat transfer analyses involved in refrigeration can be performed with steady state models, i.e. models which assume there is no net change with time in the variables of interest (or at least no signiicant net change). One dimensional steady state conduction is described by Fourier’s Law:
4 [
N$
G7 G[
(3.1)
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Heat Transfer
where: k is thermal conductivity (W m-1 K-1), A is the cross-sectional area in the direction of the heat low (m2) and dT/dx is the temperature gradient in the x-direction (K m-1) and the subscript x is to indicate the heat low in the x-direction. Note that the negative sign in Fourier’s Law is to ensure that the heat low is positive when heat lows from a higher temperature to a lower temperature (i.e. when the temperature gradient is negative), so that the Second Law of hermodynamics is not violated. When rearranged to be explicit in terms of k, Eq. (3.1) actually serves as a deinition of thermal conductivity. Data for thermal conductivity of diferent materials may be found in a wide variety of sources, including those listed at the end of this chapter. For a plane wall Eq. (3.1) may be rewritten:
7 7 4 N$ '[
(3.2)
where the subscripts 1 and 2 refer to either side of the plane wall and Dx is the thickness of the wall. In cylindrical polar coordinates Fourier’s Law may be written:
N$U
4 U
G7 GU
(3.3)
where r is the radial distance from the centreline (origin) and the subscript r indicates that heat low is in the radial direction. Note that the cross sectional area in the radial direction depends on the radius:
$U
SU/
(3.4)
where L is the length in the axial direction (m). To obtain an expression for heat low through a pipe wall we must integrate Eq. (3.3) between suitable limits ater substituting in Eq. (3.4):
4 U
³
UR
UL
4 U
NSU/
GU U
G7 GU
SN/ 7R GW 4 U ³7L
SN/
7L 7R OQ UR UL
(3.5)
where the subscripts o and i refer to the condition at the outside and inside respectively of the pipe wall. Steady state convection is described very simply by Newton’s Law of Cooling: 4 K$ 7 7
(3.5)
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Refrigeration: Theory And Applications
Heat Transfer
where h is referred to as the heat transfer coeicient (W m-2 K-1), or the ilm heat transfer coeicient. As with thermal conductivity and Fourier’s Law, Newton’s Law of Cooling actually serves as the deinition of h, i.e. the proportionality between a temperature diference and a heat lux. Experiments have shown that h is dependent on a large number of factors including the velocity and turbulence of the luid over the surface of an object and the physical properties of the luid. In practice heat transfer coeicients are oten determined from correlations of experimental data. A large number of data for low in pipes and ducts and over lat plates may be found in the literature (including the references listed at the end of this chapter). Table 3.1 gives a list of indicative values for heat transfer coeicients. h (W m-2 K-1)
Natural Convection of gases
1–50
Forced of Convection of gases
25–500
Natural Convection of liquids
10–1000
Forced Convection of liquids
50–10,000
Boiling and Condensation
2000–100,000
Table 3.1: Typical values of convection heat transfer coeicients
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It is worth noting from Table 3.1 that heat transfer coeicients due to lowing liquids (i.e. forced convection) are typically orders of magnitudes higher than lowing gases, and that heat transfer coeicients due to condensation and boiling processes are typically orders of magnitudes higher than for lowing liquids. Hence the phase change processes that take place in the condenser and evaporator are beneicial not only because of the high energy storage capacity, but also because of the high rates of heat transfer that may occur. Consider the diagram shown in Figure 3.1, of a plane wall separating two luids in which the bulk luid temperature on one side of the wall is kept constant at T∞,i, while the bulk luid on the other side of the window is kept constant at some lower temperature T∞,o (e.g. a window in a room which has the air temperature thermostatically controlled during a period when the outside air temperature remains essentially constant).
T
T∞,i Ts,o
hi
Ts,i
T∞,o ho
k
Dx
x
Figure 3.1: Schematic of a plane wall separating two luids
Note that while the temperature of the luid (say, air) a certain distance away from the window will have little dependence on x, there is a noticeable reduction in temperature as it approaches the surface of the wall, due to the presence of a boundary layer of air – a layer of air that is prevented from mixing as thoroughly with the air in the room due to friction against the surface of the window pane. Likewise there is a boundary layer on the outside of the window. A typical temperature proile of this situation is indicated by the red line in Figure 3.1. According to Newton’s Law of Cooling, the heat transferred from the air inside the room to the surface of the window is:
Q = hi A(T∞ ,i − Ts ,i )
(3.6)
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Refrigeration: Theory And Applications
Heat Transfer
where the subscript s refers to the surface of the window. A similar expression may be obtained for the low of heat between the outside surface of the window and the bulk air outside:
Q = ho A(Ts ,o − T∞ ,o )
(3.6)
he heat low through the window pane is given by Fourier’s Law:
4
N$
7V L 7V R '[
(3.7)
Since the system is at steady state (i.e. temperatures and heat lows do not vary with time) the heat low from the inside bulk air to the inside window surface must be equal to the heat low through the window pane and also to the heat low from the outside surface to the bulk air outside, i.e.:
7 7V R 4 KL $ 7fL 7V L N$ V L '[
KR $ 7V R 7f
(3.8)
From the equalities in Eq. (3.8) we can eliminate Ts,i and Ts,o to give an expression for heat low in terms of the bulk air temperatures inside and out:
A(T∞ ,i − T∞ ,o ) Q = 1 k 1 + + hi Dx ho
(3.9)
We can combine the resistances to low from the inside surface boundary layer, the pane of glass and the outside surface boundary layer in one variable called the Overall Heat Transfer Coeicient (U):
U=
1 1 1 k + + hi Dx ho
(3.10)
and Eq. 3.9 may be simpliied to
4 8$ 7fL 7fR
(3.11)
he overall heat transfer coeicient is a convenient parameter for characterising steady-state heat transfer, and is very useful for performing calculations and analyses in heat exchangers, such as a condenser or evaporator of a refrigeration system, and also for modelling heat iniltration into a refrigerator, from a variety of sources. Its value may be determined relatively simply by relatively straightforward experiments, as will be illustrated for a heat exchanger later in Example 3.1.
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3.3
Heat Transfer
Heat Exchangers
he scenario depicted in Figure 3.1 assumes that the heat low from one luid to the other is small enough so as to have negligible impact on either bulk luid temperature T∞,i or T∞,o (i.e. the two luids behave as thermal reservoirs). his assumption allows us to assume the bulk luid temperatures remain constant over prescribed time periods. his scenario is reasonable when considering heat loss through a window, for example, but is not accurate for heat exchangers, where the purpose of the heat exchanger is to change the luid temperatures. For heat exchangers we are typically interested in four temperatures, the inlet and outlet temperatures of the stream on the higher temperature side (TH,i, and TH,o) and the inlet and outlet temperatures on the lower temperature side (TC,i, and TC,o). Because the temperature of the hotter luid is not constant, but varies between TH,i, and TH,o (and similarly for the colder luid) we cannot use a simple expression like Eq. (3.11), even if we know the heat transfer area and the overall heat transfer coeicient. What we need is an expression for the average temperature diference between the two luids over the entire heat exchange surface, and the appropriate average in this case is the logarithmic mean, or more speciically in this context, the Logarithmic Mean Temperature Diference (LMTD or ∆TLM) deined by Eq. (3.12) for counter-current low (see Figure 3.2):
'7/0
7+ L 7& R 7+ R 7& L § 7 7& R · ¸ OQ ¨¨ + L ¸ 7 7 + R & L ¹ ©
(3.12)
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TH,i
Heat Transfer
Co-current flow
TC,i
TC,o
TH,o
TH,o
Counter-current flow
TC,i
TC,o
TH,i
Figure 3.2: Illustration of co-current and counter-current low in a heat exchanger
Counter-current low, in which the luids enter the exchanger at opposite ends is more eicient than co-current low, in which the luids enter the exchanger at the same end simply because the LMTD will be higher for given values of TH,i, TH,o, TC,i, and TC,o [Demonstrate this for yourself! To get the co-current form of the LMTD, simply switch the positions of TC,i, and TC,o in Eq. (3.12)]. By substituting the deinition of the LMTD into Eq. (3.11) we get a more useful equation for heat exchangers: 4 8$'7/0
(3.13)
Equation 3.13 is sometimes referred to as the Heat Exchanger Equation.
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Refrigeration: Theory And Applications
Heat Transfer
In some cases the outlet temperatures of the two streams in a heat exchanger may not be known, and hence the LMTD cannot be determined. However, using a technique known as the Efectiveness-NTU Method, the heat transferred and outlet temperatures of both streams may be determined, provided the overall heat transfer coeicient, heat transfer area and heat capacities of both streams are known. he reader is directed to the references listed at the end of this chapter for more information of the Efectiveness-NTU method. Example 3.1. A counter-current heat exchanger is used to cool a process stream from 80 °C to 35 °C, using water from a river at 15 °C. If the mass low-rate of the process stream is 40 kg s-1, its speciic heat capacity is 3.9 kJ kg-1 K-1 and the heat transfer area of the heat exchanger is 200 m2, calculate: a) the required low-rate of cooling water if the exit temperature is not allowed to rise above 25 °C (assume the speciic heat capacity of water is 4.18 kJ kg-1 K-1) b) the overall heat transfer coeicient of heat exchanger. Solution: a) he mass low-rate of the cooling water may be found by performing an enthalpy balance on both luid streams. From the process stream we can calculate the heat transferred from its change in enthalpy:
4 '+ +
P + & S + 7+ L 7+ R
u u
N: he mass low-rate of the cooling luid may then be determined from the enthalpy balance on the cooling water
4
'+ &
P & & S & 7& L 7& R 4
P &
& S & 7& L 7& R
u
NJV b) he overall heat transfer coeicient may be determined from Eq. 3.13 ater irst calculating the logarithmic mean temperature diference.
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Refrigeration: Theory And Applications
'7/0
Heat Transfer
7+ L 7& R 7+ R 7& L
§7 7 · OQ ¨¨ + L & R ¸¸ © 7+ R 7& L ¹ § · OQ ¨ ¸ © ¹ q&
Hence: 4 8$'7/0 4 8 $'7/0 u N:P .
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In Example 3.1 the luids on both sides of the heat exchange surface had temperatures varying continuously along the length of the heat exchanger; however, in the evaporator and condenser of a refrigeration system, the refrigerant temperature will not vary as signiicantly because of the phase change occurring. In fact, for irst-approximation calculations it will be reasonable to assume that the refrigerant temperature is constant at the condensing temperature (as determined from the phase diagram or refrigerant property tables) or evaporating temperature, as appropriate. Another point to note is that the need for a inite temperature diference across the heat exchange surface in a heat exchanger reduces the performance of a refrigeration system. his point is illustrated in Figure 3.3, and Example 3.2.
Figure 3.3: Schematic of the relative temperature diferences between the evaporator and condenser, superimposed on a T-S diagram for a vapour compression cycle (c.f. Fig. 2.7a).
Example 3.2: If a refrigerator is being used to maintain a temperature of 4 °C, and is rejecting heat to air at 25 °C, calculate the diference in Carnot COP based on the refrigerant temperatures and the air-side temperatures, if the LMTD of each heat exchanger is a) 5 °C, b) 10 °C.
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Refrigeration: Theory And Applications
Heat Transfer
Solution: a) From Eq. 2.18, the COP based on the external and refrigerated air temperatures is:
&235 &DUQRWDLU
7& 7+ 7&
he COP based on the refrigerant temperatures with an LMTD of 5 °C is:
&235 &DUQRWUHIULJHUDQW
7& 7+ 7&
b) With an LMTD of 10 °C the COP is:
&235 &DUQRW UHIULJHUDQW
7& 7+ 7&
Example 3.2 shows that the maximum performance of the refrigerator is decreased as the LMTD is increased. So why do we not choose to have minimal LMTD in condensers and evaporators, thereby maximising the COP? he answer can be seen by rearranging the heat exchanger equation (i.e. Eq. 3.13): $
4 8'7/0
(3.14)
For a given heat duty and overall heat transfer coeicient, the required heat transfer area (and hence size and cost of the heat exchanger) is inversely proportional to the LMTD. he temperature diference across the heat exchanger is therefore a key design variable whose value will be determined by a trade-of between the greater energy eiciency of a small LMTD against the lower costs and size of a larger LMTD.
3.4
Transient Heat Transfer
When an object (e.g. a food product) is placed into a refrigerator, we are oten interested in the time required for the object to cool to a speciied temperature, and perhaps also the instantaneous rate of heat loss from the product. his is vitally important with temperature-sensitive materials, including most biological products, where there is a risk of spoilage if the rate of temperature change is either too slow or too fast. Since the temperature change and heat transfer rates are dependent on time, we cannot use the simple steady-state equations of Sections 3.2 and 3.3. For liquids we can assume that, due to natural convection, the temperature within the liquid container is roughly uniform and therefore may be represented by one temperature. In this situation an enthalpy balance around the food product which is cooled at its surface by some medium (usually, but certainly not exclusively, air) is given by:
U9& S
G7 GW
K$ 7 7f
(3.15)
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59
Refrigeration: Theory And Applications
Heat Transfer
Rearrangement and integration of Eq. (1) with T = T0 when t = 0 and T = T(t) when t = t gives:
§ K$ ·¸ 7 W 7f 7 7F H[S ¨ W ¨ U9& ¸ S ¹ ©
(3.16)
Eq. (3.16) is oten referred to as the ‘lumped heat capacity model’ and gives a simple exponential decay relationship between temperature and time. As well as being a realistic model for liquids, it can occasionally be used for solids, provided the size of the object is small (a thickness of a few millimetres) and it is being cooled in still air. he heat load for this problem can be determined from:
§ K$ ·¸ 4 K$>7 W 7f @ K$ 7L 7f H[S ¨ W ¨ U9& ¸ S ¹ ©
(3.17)
For solids (or for highly viscous liquids) the spatial temperature variation within the object must be accounted for and a simple enthalpy balance such as Eq. (3.15) will not be adequate. For a material having uniform composition and whose thermal properties are independent of temperature, conduction within the product is governed by Fourier’s Second Law, which is a form of commonly occurring partial diferential equation called the Difusion Equation:
U& S
w7 wW
N 7
(3.18)
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Refrigeration: Theory And Applications
Heat Transfer
Assuming convection at the surface and symmetrical heat transfer, we have the following boundary conditions:
N
w7 wU
DQG N U
w7 wU
K 7 7f
U 5
(3.19)
Note that an ‘apparent heat transfer coeicient’ may be used which will include the efects of radiation (and in some cases evaporation or packaging) in addition to convection. For regular geometries in which heat transfer is only signiicant in one dimension (e.g. the sphere, the long cylinder and the plane wall) and objects being initially at some uniform temperature (T0), the solution of Eq. (3.18) with convection boundary conditions may be written generally as:
T U W {
7 U W 7f 7 7f
¦\ f
Q
Q
OQ H[S OQ )R ] Q OQ U
(3.20)
where:
)R
NW U& S 5
(3.21)
and the λn parameters are functions of the the object’s geometry and the Biot number:
%L
K5 N
(3.22)
For a sphere of radius R:
OQ FRW OQ
\ Q OQ ] Q OQ U
(3.23)
%L
VLQ OQ OQ FRV OQ OQ VLQ OQ
(3.24)
VLQ OQ U 5 OQ U 5
(3.25)
he Biot number is a very important parameter in any transient heat transfer problem involving conduction because it is the ratio of internal to external heat transfer resistance. A high Bi (e.g. Bi > 10) indicates that the heat transfer process is dominated by conduction within the product, while a low Bi (e.g. Bi < 0.1) indicates that resistance to heat transfer is dominated by resistance between the product’s surface and the cooling luid (and Eq. 3.16 may therefore be applied). Most cooling models are dependent on Bi.
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61
Refrigeration: Theory And Applications
Heat Transfer
Ater a certain time has elapsed such that Fo > 0.2, only the irst term in the ininite series in Eq. (3.20) is signiicant, hence for a sphere:
T VSK U W
7 U W 7f 7L 7f
VLQ O O FRV O VLQ OU 5 H[S O )R O VLQ O OU 5
(3.26)
Oten (particularly with refrigeration) we are interested in the centre temperature (i.e. when r = 0). In this case Eq. (3.26) reduces to:
T VSK W
7 W 7f 7L 7f
VLQ O O FRV O H[S O )R O VLQ O
(3.27)
Comparison of Eqs. (3.26) and (3.27) indicates that any of-centre temperature may simply be related to the centre temperature by the factor ζ1 (Eq. 3.25) which is independent of time. his is illustrated in Figure 3.4 which shows the cooling curves at the surface, mid-radius and centre of a sphere.
Figure 3.4. Cooling curves at the centre, mid-radius and surface of a sphere with Bi = 1.
Figure 3.4 shows that when the cooling curves at diferent positions are plotted as lnθ vs. t, they are parallel lines with diferent y-intercepts. he efect of the ζ function in Eq. 3.20 is to move the cooling curve up or down, depending on how far of centre the point of interest is. Example 3.3: An orange may be approximated as a perfect sphere having the thermal properties of water and a radius of 40 mm. If the orange is initially at a uniform temperature of 25 °C and it is placed in a refrigerator in which the air is maintained at 4 °C calculate: a) the time for the temperature at the centre of the orange to reach 10 °C b) the temperature at the surface at this time. Use the following data: h = 45 W m-2 K-1, k = 0.6 W m-1 K-1, ρ = 999 kg m-3, Cp = 4180 J kg-1. Download free eBooks at bookboon.com
62
Refrigeration: Theory And Applications
Heat Transfer
Solution: a) To determine the time required for the centre temperature to reach 10 °C, we use Eq. 3.27 where Fo (efectively the dimensionless time) is the unknown value. We can then solve for t from the deinition of Fo (Eq. 3.21). However, in order to use Eq. 3.27 we will need to know the value of λ1, which we can obtain from the Bi number via Eq. 3.23.
K5 u N (TYLDLWHUDWLRQ
%L
O
From the temperature data supplied
T VSK W
7 W 7f 7L 7f
From Eq. 3.24
y 1 (l1 ) =
4(sin 2.8895 − 2.8895 cos 2.8895) = 1.6227 2 × 2.8895 − sin(2 × 2.8895)
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Refrigeration: Theory And Applications
Heat Transfer
Rearranging Eq. 3.27:
§ T W · ¸ OQ ¨ O ¨© \ ¸¹
)R
§ · OQ ¨ ¸ © ¹
Rearranging Eq.3.21:
U& S 5 )R W N V | KRXU
u u u
Hence we predict that it will take about an hour for the centre of the orange to reach 10 °C. Note that the fact that Fo > 0.2 in this problem validates our use of Eq. 3.27 rather than Eq. 3.20, and has saved us the trouble of calculating λ2, λ3…, ψ2, ψ3… etc. b). To calculate the temperature at the surface (i.e. when r = R) of the orange ater 3691 s we observe that:
q sph ( R, t ) = q sph (0, t )
sin (l1 ) sin (l1 R / R ) sin 2.889 = q sph (0, t ) = 0.2857 × = 0.0940 l1 R / R l1 2.889
Hence:
T VSK 5 W
7 5 W 7f 7 7f
?7 5 W T VSK 5 W 7 7f 7f
u q&
he heat load for a cooling sphere without phase change and for Fo > 0.2 is given by:
sin l1 − l1 cos l1 4πR 3 rC p (Ti − T∞ ) Q sph (t ) = 1 − 3q sph (0, t ) l13 3
(3.28)
Similar expressions for dimensionless temperature and heat low may obtained for the long cylinder and the plane wall, and may be found in the sources cited at the end of the chapter.
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Refrigeration: Theory And Applications
Heat Transfer
While some items that might be placed in a refrigerated environment might be approximately spherical or cylindrical, most of them will have irregular geometries. he mathematics that would be required for analytical models of the cooling process would be excessively complex to be worthwhile; however, it is actually possible to treat the efects of geometry empirically, and independently of the efects of time. his may be seen by plotting the cooling curves of the three simple geometries (sphere, long cylinder and plane wall) for Bi = 1 (i.e. same dimensions, physical properties and heat transfer coeicient for each shape), as shown in Figure 3.5.
Figure 3.5. Cooling curves for sphere, long cylinder and plane wall with Bi = 1.
Figure 3.5 illustrates that the cooling curve for a long cylinder or plane wall could be obtained by applying a constant ‘shape factor’ to the cooling curve of the sphere (and, in fact, another factor applied to the y-intercept) provided the radius of the cylinder and the half-thickness of the wall are the same as the radius of the sphere. Hence, any geometry can have empirical shape factors determined by relatively simple experimentation; a point that will be expanded on in Chapter 6.
3.5
Summary of Chapter 3
While hermodynamics allows us to perform calculations about the necessary temperatures pressures and heat lows in refrigeration problems, we need the separate discipline of Heat Transfer to allow us to size the heat exchangers of a refrigeration system, and also to determine the transient temperatures and heat loads of products being placed in the refrigeration system to be cooled. For the former problem we used steady-state heat transfer analyses and arrived at the heat exchanger equation:
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Refrigeration: Theory And Applications
Heat Transfer
(Similar expressions to the heat exchanger equation may also be used to model heat iniltration into the refrigerated environment.) For the latter problem we used transient heat transfer analysis and arrived at the following expression:
T U W {
7 U W 7f 7 7f
¦\ f
Q
Q
OQ H[S OQ )R ] Q OQ U
which may be greatly simpliied by a number of assumptions, and where ψ and ζ (if needed) may be determined empirically. More details about the use of these models may be found in the Further Reading section.
3.6
Further Reading
ASHRAE Handbook: Refrigeration, American Society of Heating, Refrigeration and Air Conditioning Engineers, Atlanta, 2010 Çengel, YA & Ghajar, AJ, Heat and Mass Transfer: fundamentals and applications, 4th Ed., McGraw Hill, New York, 2011 Hundy, GF, Trott, AR & Welch, TC, Refrigeration and Air Conditioning, 4th Ed., Butterworth Heinemann, Oxford, 2008 Stoecker, WF & Jones, JW, Refrigeration and Air Conditioning, 2nd Ed., McGraw Hill, New York, 1986
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66
Refrigeration: Theory And Applications
Refrigerants
4 Refrigerants he vast majority of refrigerators, heat pumps and air conditioners use the vapour compression cycle – the vapour that gives its name to the cycle is a working luid called the refrigerant (even for heat pumps and air conditioners). Of course it is possible to achieve mechanical cooling without a refrigerant, but these devices make up only a very small percentage of all refrigerators, and will be dealt with in a Chapter 5. So what is required for a substance to be a refrigerant? It turns out that almost any luid can be used in a mechanical refrigeration cycle, including common-place ones such as air, water and carbon dioxide. However, some perform better than others; and of course most readers will be aware of environmental considerations such as the ozone layer and the greenhouse efect. So how does one select the best refrigerant for a task?
4.1
Desirable Attributes of Refrigerants
Generally speaking there are three basic categories of attributes we desire of our refrigerants: 1. Performance (eiciency, compatibility, cost) 2. Safety 3. Minimal environmental impact
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4.1.1
Refrigerants
Performance
he irst aspect of performance is thermodynamic eiciency; we would like the refrigerant to have a high critical point and low triple point so that it can operate within the vapour-liquid region of the phase diagram (and hence have suicient phase change in both the condenser and evaporator), and high enthalpies of vaporisation so that each gram of refrigerant can transport large quantities of heat. hese two criteria might lead us to look at small, polar molecules: small for large speciic enthalpies of vaporisation, and polar for higher critical points. One such molecule that its this description is ammonia, which is indeed one of the most eicient refrigerants, and has been used consistently almost since the dawn of mechanical refrigeration. However, it does not do so well in the safety criteria, as will be discussed later. But there other desirable physical attributes: we want a relatively high density of the vapour at the compressor inlet to minimise the work requirement, we would like high thermal conductivity for heat transfer, and we typically require miscibility with the lubricating oil of the compressor. We also need the refrigerant to be chemically stable so that its performance doesn’t change over time, or worse still, produce detrimental by-products. We want it to be non-corrosive, so that we do not need to pay for expensive, corrosion-resistant materials of construction for our refrigerator. Finally, of course, we need the refrigerant itself to be relatively cheap. 4.1.2
Refrigerant Safety
Ammonia performs excellently in a wide range of refrigeration applications; however, it is highly lammable and toxic, which means it is not suitable in domestic settings, or in devices which are susceptible to leakage, such as automobile air-conditioners. Clearly we would prefer non-lammable, non-toxic refrigerants. In the 1930s homas Midgley discovered that a class of compounds containing one or two carbon atoms, with varying numbers of chlorine and luorine atoms attached were very efective refrigerants. hese chemicals, later to be referred to as chloro-luoro-carbons, or CFCs seemed to be ideal; they had desirable thermodynamic properties, and they were non-toxic, non-lammable and non-corrosive. For 50 years or so they were used abundantly, particularly R11 (trichloroluoromethane CCl3F2), R12 (dichlorodiluoro-methane CCl2F2) and R22 (Chlorodiluoromethane, CHClF2). In the late 1970s, however, scientists Rowland and Molina argued that the chlorine in CFCs was destroying ozone in the stratosphere. Ater some initial opposition, this theory was accepted as being correct and Rowland and Molina shared the Nobel Prize in 1995 for their work. Clearly while being eicient and safe in terms of direct exposure to humans, CFCs have a negative environmental impact.
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Refrigeration: Theory And Applications
4.1.3
Refrigerants
Environmental Impact
here are two aspects of the environmental impact of a refrigerant; irstly there is the direct impact of the refrigerant leaking from a system and escaping to the atmosphere; secondly there is also the impact from the extra carbon load on the environment from the extra fossil-fuel that needs to be burned by a less-eicient refrigerant compared to a more eicient refrigerant. here are two major measures of the environment impact of a refrigerant: the ozone depleting potential (ODP) and the Global Warming Potential (GWP). he ODP is based solely on the impact of the release of the refrigerant into the atmosphere; however the GWP is based not only on the direct release of the refrigerant into the atmosphere, but also the energy consumption for a given refrigeration load by that particular refrigerant. Sometimes the term Total Equivalent Warming Impact (TEWI) is used in GWP calculations. In 1987 the Montreal Protocol was signed by a large number of countries, and the phase-out of refrigerants containing chlorine began in order to protect the ozone layer, and has continued successfully, to the point that CFCs have almost disappeared from use in the Developed World. How could they be replaced? Ideally, ‘drop-in’ replacements could be found such that an existing refrigeration system could be drained of its old, CFC refrigerant and be replaced by a non-CFC. One highly successful example was R134a (1,1,1,2-Tetraluoroethane, CH2FCF3) as a drop-in replacement for R12; however being a compound containing luorine (a so-called ‘F-gas’), which have direct GWP values of several thousand times that of carbon dioxide, its use has been scheduled for phase-out by signatories of the Kyoto Protocol. So what’s let? Ammonia is eicient and environmentally friendly, but hazardous. CFC’s are eicient and safe but destroy the ozone. F-gases such as R134a are eicient and safe but apparently contribute signiicantly to global warming. Which refrigerants are suitable in the modern age?
4.2
Refrigerants after the Montreal and Kyoto Protocols
To date no single refrigerant has been discovered that satisies all the criteria desired of the ideal refrigerant. Perhaps R12 came the closest to being the ideal refrigerant before its environmental impacts were discovered, but since then no single compound can claim to be as dominant as it once was. Instead diferent refrigerants tend to be used for diferent tasks; the common ones are discussed briely here. 4.2.1
Ammonia
Ammonia, as mentioned previously, was one of the very irst refrigerants to be used with the vapour compression cycle. It has been in continuous use since then, although its popularity saw a decline in the middle of the 20th century due to the widespread use of CFCs. Since the signing of the Montreal Protocol, however, its use has recovered. As discussed above, it fares very well against the performance criteria but poorly in the safety criteria. However, given that it is part of the nitrogen cycle it performs excellently again against the environmental criteria, having both zero ODP and zero GWP.
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Refrigeration: Theory And Applications
Refrigerants
Today it is the dominant refrigerant on the industrial scale, thanks to its high eiciency, low cost and minimal environmental impact. With advances in the design of refrigeration components, leakage is less of a problem. In addition, the use of non-lammable secondary refrigerants (i.e. refrigerants that are cooled by the primary refrigerant, before in turn cooling the load) has reduced safety concerns where lammability is a signiicant risk. 4.2.2
Carbon Dioxide
Like ammonia, carbon dioxide was one of the irst refrigerants to be used in the vapour-compression cycle; however it is not as eicient as ammonia, having quite a low critical point. It performs better than ammonia against the safety criteria, being non-lammable and less toxic (although it may still cause fatal poisoning), and has zero ODP and relatively low (some would argue zero) direct GWP. It disappeared from widespread use ater the advent of the CFCs in the 1930s, but in recent years has made a strong recovery with the development of the trans-critical vapour-compression cycle. Its use is predicted to increase, both for low temperatures on the industrial scale, and also for commercial use, such as in supermarket display cabinets.
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4.2.3
Refrigerants
Hydrocarbons
Like carbon dioxide, hydrocarbons were tested as refrigerants before the introduction of CFCs, but their high lammability saw them fall out of favour. hey too have seen more widespread use since the Montreal and Kyoto Protocols to the point where iso-butane (R600a, CH(CH3)3) in particular is widely used in domestic refrigeration in Northern Europe. It has been predicted that the use of hydrocarbon refrigerants will increase in the future as safety features of refrigeration systems are improved. 4.2.4
Hydro-luorocarbons (HFCs)
As the chosen successor to R12, R134a is still in widespread use, particularly for smaller applications such as domestic refrigerators and domestic and automobile air conditioners. Because it has high GWP, there has been pressure for its phase-out by signatories of the Kyoto Protocol, but since there are many countries who are not signatories, its use (along with other HFCs) looks set to continue for several years to come. 4.2.5
Blends
Refrigerant blends have been used since the time of CFCs, as people attempted to tailor the performance and safety of the refrigerant to meet a desired task. For example, an eicient but lammable refrigerant may be blended with a slightly less-eicient, non-lammable refrigerant to reduce the overall lammability of the mixture. Ideally azeotropic mixtures (i.e. those whose composition does not vary between the liquid and vapour phases) should be used, since their properties are not altered as a result of leakage. Common examples of blended refrigerants are R502, which is a blend of the CFCs R22 and R115 (CClF2CF3) and R404A, which is a blend of the HFCs R134a, R143a (CH3CF3) and R125 (CHCF5). HFC blends continue to be used in commercial refrigeration, but are subject to political pressure for their phase-out.
4.3
Summary of Chapter 4
he ideal refrigerant has a high critical point, high enthalpy of vaporisation, is miscible with lubricating oil, is cheap, is non-lammable, is non-toxic, has zero ODP and GDP, amongst other desirable criteria. Unsurprisingly, perhaps, no single refrigerant satisies all these desirable criteria. Since the signing of the Montreal and Kyoto Protocols, the trend has been away from the synthetic, chlorine and luorinecontaining refrigerants towards natural refrigerants such as ammonia, carbon dioxide and hydrocarbons. Some synthetics, R134a in particular, look set to remain in widespread use for the foreseeable future.
4.4
Further Reading
Hundy, GF, Trott, AR & Welch, TC, Refrigeration and Air Conditioning, 4th Ed., Butterworth Heinemann, Oxford, 2008 Pearson, SF, Refrigerants Past, Present and Future, Proceedings of the 21st International Congress of Refrigeration, Washington DC, 2003
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Refrigeration: Theory And Applications
Refrigeration without a Refrigerant
5 Refrigeration without a Refrigerant If a suiciently cold natural environment is not available to cool an object, then in order to achieve a cooling efect one has to be able to change a body’s temperature without the transfer of heat (since heat will only low from a higher temperature to a colder temperature). he vapour compression and sorption refrigeration cycles rely on gas expansion to reduce the temperature of the refrigerant. However, there are several other options.
5.1
Evaporative cooling
he human body is cooled by water (sweat) evaporating from the skin. his same principle may be applied to achieve air cooling, and is particularly efective in dry climates. here are indications from ancient paintings that as early as the time of the Pharaohs in Egypt evaporative cooling was used in homes, as earthenware pitchers were illed with water which saturated the clay and evaporated from the surface. Today there is a thriving commercial market for evaporative coolers, particularly for people who live on or near a desert. Obviously, evaporative cooling is limited to a relatively narrow range of temperatures, and is most efective for air-conditioning applications. he cooling efect is directly proportional to the diference in humidity between the air before and ater it is sprayed with water, so evaporative cooling will not be feasible in humid climates. he reader might argue that the water used in evaporative cooling is a refrigerant; however, it is not a working luid in the common sense of the term, which is why it is included in this chapter. In a dry climate, all that is needed for an evaporative cooling system is water source, a small pump to pass the water through an atomising nozzle, and a fan to circulate the cooled air. Misting fans are an example of a very simple, portable evaporative cooling device. In very dry climates the increased humidity of the air from the water spray adds to human comfort. In climates that are not particularly dry the air will most likely need to be dehumidiied prior to being sprayed with water in order that there is a suicient driving force for the evaporation process, and also to prevent the need to humidify the air above 85%, which would make it uncomfortable to humans. Oten desiccant systems are used for dehumidiication, sometimes in the form of wheels, and sometimes in the form of stationary beds. he addition of the dehumidifying process increases the power requirement of the fan, since the pressure drop through the desiccant will be signiicant. Also, the desiccant will need to be regenerated, typically by heating. A number of prototype devices have been developed which use photovoltaics to drive the pump and fan, and solar thermal energy to regenerate the desiccant, thereby producing a stand-alone system, even in climates with moderate humidity.
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Refrigeration: Theory And Applications
Refrigeration without a Refrigerant
he advantage of evaporative cooling over vapour-compression air-conditioning is the relatively low running cost, since no gas is being compressed (the water pump and fan use orders of magnitude less energy than a compressor), and oten very low installation and maintenance cost. he disadvantages, apart from the requirement of low humidity and a narrow range of temperatures, are that warm, still water is an ideal breeding environment place for insects, such as mosquitoes and bacteria, such as legionella which causes Legionnaires Disease. For this reason a number of systems use indirect cooling, enclosing the sprayed water via a heat exchanger so that any potential contaminants won’t be breathed in by humans. Indirect systems are less eicient and more complex, which is the trade-of for their increased safety.
5.2
Peltier-Seebeck efect (thermoelectric devices)
he Peltier-Seebeck efect describes the relationship between temperature and voltage that occurs when two dissimilar conductors (typically metals) are connected at two separate junctions. If the two junctions are held at dissimilar temperatures then a voltage diference will exist between the two junctions, and this phenomenon is known as the Seebeck efect. he Seebeck efect may be used to measure temperature since the voltage generated is proportional to the temperature diference between the two junctions. Temperature sensors that make use of the Seebeck efect are known as thermocouples, and they are typically cheap and very versatile; although are not as accurate as resistance thermometers.
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Refrigeration: Theory And Applications
Refrigeration without a Refrigerant
Alternatively the voltage generated by the Seebeck efect may be used to run a motor. A large number of thermocouples grouped together and operating between the same temperatures is known as a thermopile, and may be used to measure temperatures, or as a thermo-electric engine. A thermo-electric engine is one which employs the Seebeck efect to generate work from a sustained temperature diference. For example, if a thermal hot spring exists close to a cold river, a thermo-electric engine might be used to power a fan simply by having one junction in the hot spring and the other junction in the cold river. he Peltier efect is essentially the Seebeck efect in reverse. If a voltage diference is applied between the two junctions of a thermocouple, one junction will increase in temperature while the other junction will decrease in temperature. he low temperature junction of the Peltier cooling is maintained by the continuous supply of power, even as it absorbs heat from its surroundings. hus the Peltier efect ofers us an incredibly simple cooling method, and allows us to produce cooling devices having no moving parts, which can be of any size or shape. Peltier coolers have a wide range of niche applications, particularly in electronics and in research laboratories. Figure 5.1 shows a demonstration model of a thermo-electric device at the University of Waikato. he thermo-electric unit (thermocouple) is sandwiched between two aluminium legs. If the device is switched to the ‘engine’ setting, then the fan will run if one leg is placed in ice water and the other is placed in boiling water. If the device is switched to the ‘Peltier’ setting and a DC power supply (up to 5V for this device) is attached to the electrodes, then one of its legs will increase in temperature, while the other will decrease.
^ǁŝƚĐŚ
&ĂŶ
ůĞĐƚƌŽĚĞƐ
dŚĞƌŵŽͲĞůĞĐƚƌŝĐƵŶŝƚ ůƵŵŝŶŝƵŵůĞŐƐ
Figure 5.1: Thermo-electric device
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Refrigeration: Theory And Applications
Refrigeration without a Refrigerant
So why are Peltier coolers not in more common use? he simple answer is they have very low thermodynamic eiciency – of the order of 10–15 % of Carnot eiciency. his limits their application to the small scale, where their ineiciency is more than compensated by their practicality. Some commercial units are available and research eforts are continuing with the goal of increasing their eiciency, but in the foreseeable future, they will be limited to small, niche applications.
5.3
Magneto-Caloriic Efect (Magnetic Refrigeration)
he magneto-caloriic efect describes changes in the temperature of a (solid) medium when it is placed in a changing magnetic ield. he temperature change occurs as a result of the entropy reduction that is caused by the magnetic dipoles of the atoms in the solid coming into alignment as a result of the applied magnetic ield. Alloys of the element gadolinium (Gd) show a particularly noticeable temperature change when a magnetic ield is applied. To exploit the magneto-caloriic efect in a refrigeration cycle, the magneto-caloriic material (oten in the form of a rotor) is successively exposed to magnetic ields and heat exchange environments in an analogous manner to the vapour compression cycle. Beginning with the rotor in an unmagnetised state at low temperature, the rotor is magnetised adiabatically (i.e. in an insulated environment) such that its temperature increases (analogous to the adiabatic compression process). At the end of the magnetisation process the rotor enters a heat exchanger where it rejects its heat in an isomagnetic state (analogous to the condensation process). Subsequently it is de-magnetised adiabatically, which lowers its temperature (analogous to the expansion process). Finally it absorbs heat at the lower temperature (analogous to the evaporation process), before the cycle is repeated. Magnetic refrigeration saw its earliest practical use in low-temperature (cryogenic) applications; however, more recently a lot more efort has been put into developing units for room-temperature. By contrast with thermo-electric devices, magnetic refrigerators can be very thermodynamically eicient, provided the heat absorption and heat rejection temperatures do not vary too signiicantly. his eiciency, along with the fact that there is no refrigerant vapour to escape into the atmosphere means that magnetic refrigeration is a very environmentally friendly option. It is also very quiet, since there is no compressor, and like thermo-electric devices has relatively few moving parts. For these reasons there are hopes that the technology will continue to be developed to the point that it may one day become the standard method of refrigeration in small-scale applications such as in domestic settings or automobile air-conditioning.
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Refrigeration: Theory And Applications
Refrigeration without a Refrigerant
However, the magnetic refrigerator does sufer disadvantages, particularly when compared to the vapour compression cycle. he temperature diference between magnetised and unmagnetised states is limited which means that if there is a signiicant diference between the heat absorption and heat rejection temperatures then a cascade design may have to be employed. Permanent magnets also have limited ield strength, which imposes a relatively low upper limit to the rate at which heat may be absorbed, since electro-magnets would make the overall cost restrictive. But perhaps the biggest restriction is due to the low rates of heat transfer that occur in the heat exchangers, where rates are orders of magnitude lower than rates encountered with evaporating liquids and condensing vapours. Also the heat is not transferred isothermally, as is mostly the case in evaporators and condensers, which greatly reduces the logarithmic mean temperature diference of each exchanger. For these reasons, even if magnetic refrigeration devices come in to common usage, it is probable that they will be limited to small applications.
5.4
Thermo-acoustic efect (acoustic refrigeration)
Inasmuch as sound waves are luctuations in pressure within a luid medium (usually a gas), there will be temperature luctuations associated with these pressure luctuations. If the pressure luctuations can be made to be large enough, the accompanying temperature luctuations may be exploited to achieve refrigeration.
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A schematic of an acoustic refrigerator is shown in Figure 5.2. An ultrasonic, high-amplitude sound generator (essentially an audio speaker) is placed at one end of a pressurised resonator tube and is used to generate a standing wave. he length of the resonator tube is designed to be one half-wavelength of the generated sound wave at the desired frequency (hence the efect is analogous to plucking a guitar string). Near the sound generator end of the tube is a stack of parallel, low-conductivity plates that make up the regenerator.
Figure 5.3: Schematic of an acoustic refrigerator
Let us consider what happens to a small volume of gas as it travels between the regenerator plates. As the soundwave moves the volume from the cold side of the stack to the hot side it is compressed adiabatically, and so its temperature increases so that it can exchange heat with the luid in the hot heat exchanger at constant pressure (isobarically but not isothermally), but with a loss in temperature. he gas is then moved back from the hot side to the cold side and expands adiabatically so that it is at a lower temperature than the heat exchange luid in the cold heat exchanger, where again it transfers heat isobarically, and the cycle repeats. In principle, the thermodynamic eiciency of acoustic refrigerators could be very high, and like Peltier coolers and magnetic refrigerators they have few moving parts and have no refrigerant to cause ozone depletion or global warming. However, in practice their performance is greatly limited by the eiciency of the heat exchangers, which, similar to magnetic refrigerators, sufers from low heat transfer rates and low logarithmic mean temperature diferences, and so its application would be limited to the small scale. Currently it is not considered to be as promising an alternative to vapour compression as magnetic refrigeration.
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Refrigeration: Theory And Applications
5.6
Refrigeration without a Refrigerant
Summary of Chapter 5
here are alternatives to refrigerants for achieving cooling efects; however, none can compete with the vapour compression cycle for medium to large scale application or for wide temperature ranges. Evaporative cooling and thermo-electric devices each have their niche and magnetic refrigeration is expected to gain popularity in the near future. hermo-acoustic devices are largely only at the development stage.
5.7
Further Reading
Paek, I, Braun, JE & Mongeau, L, Evaluation of standing-wave thermoacoustic cycles for cooling applications, International Journal of Refrigeration, 30, 1059–1071, 2007 Qureshi, BA & Zubair, SM, A comprehensive design and rating study of evaporative coolers and condensers. Part I. Performance evaluation, International Journal of Refrigeration, 29, 645–658, 2006 Vasile, C & Muller, C, Innovative design of a magnetocaloric system, International Journal of Refrigeration, 29, 1318–1326, 2006 Wetzel, M & Herman C, Design optimization of thermoacoustic refrigerators, International Journal of Refrigeration, 20, 3–21, 1997 Yu, BF, Gao, Q, Zhang, B, Meng, XZ, & Chen Z, Review on research of room temperature magnetic refrigeration, International Journal of Refrigeration, 26, 622–636, 2003 Zhang, HY, A general approach in evaluating and optimizing thermoelectric coolers, International Journal of Refrigeration, 33, 1187–1196, 2010
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Refrigeration: Theory And Applications
Part 2: Applications
Part 2: Applications
( Photo Courtesy of Fisher & Paykel Appliances Ltd)
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Refrigeration: Theory And Applications
Chilling and Freezing
6 Chilling and Freezing Food preservation is required due to the fact that there is typically a time lag between when a food is harvested and when it is consumed. Grains, fruits and vegetables, and animal products tend to be produced seasonally, while their consumption is relatively steady year-round. And even if production was steady, due to urbanisation time is required for the food to be transported from the rural areas where it is produced to the cities were the majority of it is consumed. Without some means of preservation, foods, particularly those with high moisture contents, are susceptible to contamination from micro-organisms including yeasts, moulds, fungi, bacteria and viruses. Even in the absence of foreign microbes, foods may still spoil due to the activity of enzymes and other biochemical processes within the food itself. Worldwide, refrigeration and drying are probably the most common methods for preserving food. Refrigeration achieves preservation by lowering the temperature such that microbial populations do not grow at signiicant rates, and biochemical processes are slowed. Drying achieves preservation by lowering the moisture content to a point at which most microbes cannot survive. Of these two techniques, however, refrigeration has much less impact on the colour, structure and lavour of the food, and is therefore preferred as a preservation means for most foods, particularly in the Developed World. Drying (particularly sun-drying) is a lower-cost alternative for Developing Countries, particularly in rural settings.
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Chilling and Freezing
It has been estimated in that in the irst decade of the 21st Century about 360 million tonnes of perishable food was lost every year due to insuicient use of refrigeration, or poorly designed refrigeration systems. With the world’s population continuing to increase, and all the available arable land currently being used, refrigeration is going to be relied on more and more to reduce wastage and ensure the world’s population is suiciently nourished. Food refrigeration is typically separated into two categories depending on whether any ice forms. Refrigeration to temperatures above the initial freezing point of food is called chilling; refrigeration below the initial temperature of the food is called freezing. he reason for this distinction is that it is oten vital for the quality of the food that it is treated properly, e.g. most fruits and vegetables will sufer irreversible tissue damage if ice crystals are formed, and hence they must not be frozen. he physical mechanisms involved in chilling and freezing are also quite diferent, which is a further reason to analyse them separately. By contrast with the domestic situation, industrially, the process of temperature reduction (‘chilling’ or ‘freezing’) is oten (but not always) performed in a diferent device/room than the process of temperature maintenance (‘cool’ or ‘cold storage’). Typically a devoted chiller/ freezer will have a relatively small product space, and relatively large refrigeration unit, while the cool/cold store will have a higher product space and comparatively small refrigeration unit.
6.1
Estimating Chilling times of food products
Once raw foods have been harvested (here ‘harvesting’ is used as an inclusive term for all foods meaning the process of extracting them from their natural environment) there is usually a relatively narrow window during which time they must be cooled from their harvested temperature to the storage or further processing temperature. Generally the cooling process is as fast as possible; however, the biochemical/ physiological make up of some foods places an upper limit on the rates at which they may be cooled. As will be discussed in Chapter 7, diferent foods have diferent requirements, and it is important that each type of food is cooled optimally in order to reduce product wastage, and maximise proit for the producer. It is helpful if we have some way to predict how long a food product will take to cool under certain conditions since this well help us to design or select a suitable cooling regime. Recall that in Chapter 3 we discussed the cooling of regularly shaped objects, and mentioned that irregularly shaped objects could be modelled in a similar manner. For liquid foods we may simply use Eq. 3.16 (Chapter 3), provided we can determine the value of h (which may oten be measured by performing a relatively straightforward experiment). For highly viscous or solid foods we use modiied forms of Eq. 3.20 or, preferably, only the irst term of the ininite series:
T U W {
7 U W 7f 7 7f
\ O H[S O )R ] O U
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(6.1)
Refrigeration: Theory And Applications
Chilling and Freezing
If we plot lnθ vs. t for Fo > 0.2, as we did in Figures 3.4 and 3.5, we will get straight lines, which may be modelled by:
OQ>T U W @ D E W
(6.2)
where a and b, the intercept and slope of the cooling curve, are functions of λ1, i.e.
a = ln(y 1 ) + ln(z 1 )
(6.3)
b=−
(6.4)
l12 k
rC p R 2
From Eq. (6.2) we see that the inluence of the object’s shape (manifested by the parameters a and b) can be treated independently from the efect of time. Hence for any shape, if we are able to determine these shape-related factors, we can use Eq. (6.2) as the cooling model, provided there is no phase change (i.e. chilling processes only). he factors a and b can be determined empirically as a function of Bi, and this may be the simplest method for their determination for some shapes. Recall from Chapter 3 that the Biot number measures the relative resistance of heat transfer to or from the surface to the resistance to heat transfer from the centre of the object to its surface. It is a function of the product’s thickness, its thermal conductivity and the heat transfer coeicient at the product’s surface. herefore, the range of Bi considered when measuring a and b should relect the range of cooling conditions likely to be encountered (i.e. if the product is to be chilled in air, the range of Bi should relect the range of air velocities likely to be encountered). he cooling trials that would be required to determine a and b are relatively simple to perform; however, given the need to perform measurements over a range of Bi, a large number would need to be performed for a single product, which would be time-consuming and therefore expensive in a commercial setting. Fortunately, in many situations the slope and intercept of the cooling curve may be predicted. In practice a modiied form of Eq. (6.2) is used: OQ T W
OQ M W I
(6.5)
he physical interpretation of the parameter f (oten referred to as the ‘f-factor’) is that it is the time required for the dimensionless temperature to decrease by a factor of 10 (which is why the factor 2.303, which is equal to ln(10), is present in Eq. (6.5)). Note that the j-factor is given a subscript ‘0’ to indicate that it relates to the centre temperature, and a diferent factor will be required for of-centre temperatures. he f-factor applies regardless of position within the object, as is illustrated by the parallel slopes of the cooling curves at diferent positions in a sphere which is shown in Figure 3.4.
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Chilling and Freezing
For the centre of a sphere, the f and j0 parameters may be determined by comparing Eq. (6.5) with Eq. (3.27):
j0 = f =
4(sin l1 − l1 cos l1 ) 2l1 − sin( 2l1 )
(6.6)
2.303rC p R 2 kl12
(6.7)
he f and j0 parameters for the long cylinder and plane wall may be determined in a similar manner; however, for more complex shapes the determination of f and j0 will not be as trivial an exercise. he literature contains several methods for predicting their values. he relatively simple procedure of Hayakawa and Villalobos for determining the centre and/or mass average temperature is outlined here (and is also covered in the ASHRAE Handbook of Refrigeration). Firstly the object must be analysed in such a manner that the shortest distance (L) between the centre and the surface is identiied (the radius in the case of the sphere) and from this a factor P1 is deined:
P1 =
S1 πL2
(6.8)
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Chilling and Freezing
where S1 is the cross-sectional area containing L. Next the area S2 containing L orthogonal to S1 is used to determine P2:
P2 =
S2 πL2
(6.9)
In some situations it may be simpler to use an alternative deinition for P2:
P2 =
3V 4πP1 L3
(6.10)
Note that the values of P1 and P2 will be unity for a sphere. In essence this process seeks to compare the cooling rate of a particular shape with that of a sphere by introducing the appropriate shape factors. From P1 and P2 a geometry factor G is calculated:
*
3 3
(6.11)
he λ1 parameter may then be approximated from: OQ O
OQ * OQ %L
OQ * OQ %L OQ * OQ %L OQ * OQ * OQ %L OQ %L
(6.12)
Equation (6.12) applies for 0.25 ≤ G ≤ 1.0 and 0.01 ≤ Bi ≤ 100. he jm factor (the j-factor for the mass average temperature) can be estimated from Eq. (6.13):
j m = 0.892 exp(−0.0388l12 )
(6.13)
An estimate of the j0 may be obtained from jm and vice versa. To summarise this method the following steps should be taken to estimate the chilling time of a complex, or irregularly shaped food (provided 0.01 ≤ Bi ≤ 100): 1. Obtain thermal properties of food product and heat transfer coeicient of cooling luid 2. Calculate Bi from Eq. (3.22) with R = L (the shortest distance between centre an surface) 3. Estimate S1 and S2 and calculate P1 and P2 from Eqs. (6.8) and (6.9) 4. Determine G from Eq. (6.11) and then λ12 from Eq. (6.12) 5. Calculate f from Eq. (6.7) with R = L and use Eq. (6.13) to calculate j 6. Finally use a rearranged form of Eq. (6.5) to calculate the chilling time:
W
§T · I OQ ¨¨ ¸¸ © M ¹
(6.14)
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Refrigeration: Theory And Applications
Chilling and Freezing
An alternative approach which will not be presented here is to employ the equivalent heat transfer dimensionality (refer the ASHRAE Handbook of Refrigeration listed in the Further Reading Section) which is slightly more elaborate, but is based on parameters that may, in some cases, be easier to identify than L, S1 and S2. For greater accuracy than may be expected from these semi-empirical methods for estimating chilling times, numerical methods are required. As might be expected, there are several sotware packages that have been developed speciically for calculating cooling times and heat loads. An example is the Food Product Modeller™ package that has been developed by AgResearch Ltd in New Zealand. Example 6.1: Estimate the time required for a cucumber which has a diameter of 70 mm and a length of 200 mm, to cool from an initial uniform temperature of 35 °C to a mass average temperature of 4 °C when placed in a refrigerator set to maintain an air temperature of 2 °C, assuming a heat transfer coeicient of 50 W m-2 K-1. Solution: It is useful in any transient heat transfer problem to calculate Bi initially. For irregular shapes the Bi is based on the shortest path from the centre to the surface of the object, and in this case is simply the radius. However, irst we need to know the thermal conductivity of cucumber. Data for thermal properties of foods is available from a number of sources, including the ASHRAE Handbook of Refrigeration and the Food Properties Handbook (see Further Reading) especially for fruit vegetables, meat, poultry and dairy products. Where data are not available for a food (i.e. for a processed food), its thermal properties may be predicted from composition data, using models that are typically available from the same sources as the data. For high water-content foods such as fruits and vegetables, using the properties of water will oten be suitable for a irst approximation. In the case of cucumbers, data from the sources mentioned above are as follows: k = 0.59 W m-1 K-1, ρ = 950 kg m-3, Cp = 4090 J kg-1 K-1. Hence:
%L
K5 N
u
A schematic of the cucumber is shown in Figure 6.1, in which the areas S1 and S2 are indicated. We can assume that the cucumber has a perfectly circular cross-section in which case S1 will be equal to the cross-section area of a circle with a radius of 0.035 m, and P1 will be unity (by inspection of Eq. 6.8).
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Chilling and Freezing
S1 S2
Figure 6.1: Schematic of the cucumber in Example 6.1
Cucumbers have rounded ends; however, since the length of the cucumber is several time greater than the diameter, the rate of heat transfer down the axis of the cucumber will not be as great as in the radial direction, so it will be suicient for this sort of estimate to assume that the cross sectional area orthogonal to the cross-sectional area in the direction of the radius is simply the length of the cucumber multiplied by the diameter, i.e.:
6
u P
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Chilling and Freezing
Hence, from Eq. 6.9:
6 S/
3
S
From Eq. 6.11:
*
3 3
u u
From Eq. 6.12, λ12 = 3.53. From Eq. 6.7:
U& S 5 NO
I
u u u u
V
From Eq. 6.13:
MP
H[S O H[S u
he dimensionless temperature is:
T
7 W 7f 7 7f
From Eq. 6.14:
W
§T · § · I OQ ¨ OQ ¨¨ ¸¸ ¸ V © ¹ © M ¹
Hence we would expect the cucumber to take approximately 1½ hours to cool. Note that in this problem we considered a single cucumber being chilled. In reality cucumbers would be cooled in bulk, and the physical (i.e. k, ρ and Cp) and transport (i.e. h) properties involved require more attention, but are beyond the scope of this text
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6.2
Chilling and Freezing
Estimating heat loads of food products
Calculation of the heat load of a refrigeration process depends to some extent on the design of the refrigerator and in particular whether it is run under batch or continuous operation. For a continuous process (e.g. tunnel chiller where product passes through the chiller on a conveyer belt), it will probably be suicient to divide the enthalpy change between the inlet and outlet by the residence time of the product in order to determine the average load:
4
U9& S 7L 7f W
(6.15)
In reality the cooling load will vary along the length of the tunnel, but Eq. (6.15) will oten be suicient as an estimate. For a batch process (e.g. a carcass chiller, where the carcasses are placed in a refrigerated room, let there for a length of time), it is helpful to be able to model time-variable load. his may be achieved based on parameters calculated when estimating the chilling time. he time-variable heating load up to the point in time where:
W
(6.16)
I ORJ MP
may be calculated from:
4 U9& S 7L 7f
I ORJ MP
(6.17)
ater which time:
4
6.3
§ · ¸ I ¸¹ ©
U9& S 7L 7f H[S ¨¨
(6.18)
Freezing and Thawing Time Prediction
A standard temperature history (i.e. cooling curve) of a chilling process follows a relatively simple exponential decay curve, as illustrated in Figures 3.4 and 3.5. By contrast, the temperature history of a freezing process has cusps and cannot be modeled simply by a continuous function. Figure 6.2 shows the freezing curves at three diferent positions in a pail of strawberry pulp.
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Chilling and Freezing
Mean
20
Centre 15
Edge
10
temperature (°C)
5 0 -5
0
5
10
15
20
25
30
-10 -15 -20 -25 -30 -35 time (hours)
Figure 6.2: Temperature histories at three diferent locations in a pail of strawberry pulp
Initially, the freezing curves follow an exponential decay, since above the initial freezing temperature it is simply a chilling process. Note that unlike pure water which has a distinct freezing temperature above which water is in the liquid state and below which water is in the frozen state, the freezing point of a solution only has a distinct starting point. Below the initial freezing point water still may exist in the liquid state, while water elsewhere has crystallised.
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Chilling and Freezing
At the initial freezing temperature there is a noticeable temperature plateau at the centre and mass average positions, while the absolute magnitude of the slope of the surface (edge) temperature is signiicantly less than for the slope above the initial freezing temperature. hese efects are due to the release of latent heat (or, more properly, enthalpy of fusion) as the ice crystals form. he latent heat efects accompanying the formation of ice in a food product complicate the heat transfer analysis when compared to a chilling process; nevertheless a similar empirical approach to the one outlined in Section 6.1 may be employed. here are many freezing models within the literature, most of which have been based on Plank’s method from the early 20th Century; however, several studies have recommended that Pham’s method provides the greatest accuracy for a range of shapes and hence will be outlined here. he freezing time (tf) may be calculated from:
WI
/ § '+ '+ ·§ %L · ¨ ¸¨ ¸ ¹ '7 ¸¹© ( I K ¨© '7
(6.19)
where Ef is the equivalent heat transfer dimensionality for freezing, which has values of 1, 2 and 3 for the plane wall, long cylinder and sphere respectively. Note that the plane wall and sphere represent the lower and upper limits respectively (can you see why?), and any irregular shape should have an E value between 1 and 3. ∆H1 and ∆T1 represent the contributions from the sensible heat above freezing, given by Eq. 6.20 and 6.21 respectively and ∆H2 and ∆T2 represent the latent heat contributions, given by Eq. 6.22 and 6.23:
'+
'7 '+
'7
U X & SX 7L 7 IP
7L 7 IP
(6.20)
7f
(6.21)
U I >'+ I & S I 7 IP 7F @
7 IP 7f
(6.22) (6.23)
he subscript u refers to the properties of the unfrozen product and Tfm is essentially the mid-point of the freezing process, and may be estimated by:
7 IP
7F 7f
(6.24)
Where Tc is the inal temperature of the product, and T∞ is the temperature of the cooling medium. For irregularly shaped objects Ef may be estimated by:
(I
%L %L 3 3 3 3 %L %L
where P1 and P2 were deined by Eqs. (6.9) and (6.10). Download free eBooks at bookboon.com
90
(6.25)
Refrigeration: Theory And Applications
Chilling and Freezing
It is worth noting that thawing is not simply the reverse process of freezing since the formation of ice crystals oten has an irreversible efect on the food’s structure. Cleland et al. developed a simple, semiempirical method for predicting thawing times:
WW
/'+ [ [ %L ( I K 7f 7 I
(6.26)
where:
x1 = 0.7754 + 2.2828x 3x 4
(6.27)
x 2 = 0.5(0.4271 + 2.1220x 3 − 1.4847x 32 )
[
[
(6.28)
U X & SX 7f 7 I '+
(6.29)
U I & S I 7 I 7L '+
(6.30)
and ∆H10 is the volumetric enthalpy change of the product between 0 and -10°C (which is signiicant, because it is the temperature range during which the fraction of ice in the food changes most rapidly). he average heat load for a freezing process may be determined by the total heat load divided by the freezing time:
V Q f = (DH 1 + DH 2 ) tf
(6.31)
Where ∆H1 and ∆H2 were deined by Eqs. 6.20 and 6.22. Methods for estimating time-variable heat loads during freezing may be found in the ASHRAE Handbook of Refrigeration. Example 6.2: he frozen contents of a carton of lean beef cuts, 400 mm × 600 mm × 120 mm is thawed in still air. he uniform, initial temperature of the beef is -40 °C and the thawing air is at 10 °C, while the heat transfer coeicient is 15 W m-2 K-1. Calculate the time required for the mass average temperature of the block to reach 5 °C. Solution: Obtaining data from the ASHRAE Handbook of Refrigeration, we have: ru = 1075
kg m-3, rf = 1018 kg m-3, Cp,u = 3520 J kg-1 K-1, Cp,f = 2110 J kg-1 K-1; ku = 0.49 W m-1 K-1, kf =
1.6 W m-1 K-1, Tf = -2 °C, DH10 = 210 MJ m-3.
Next we calculate Bi. he shortest distance between the centre and the surface is 60 mm (i.e. half the smallest of the three dimensions of the block). he thermal conductivity of the beef is quite diferent depending on its state; however, we will chose the frozen beef thermal conductivity, since the majority of the warming process occurs while there is at least some ice. Hence:
%L
K/ N
u
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Chilling and Freezing
In order to calculate the equivalent heat transfer dimensionality, we need to determine the parameters S1, S2, P1 and P2 in the same manner that we did in Example 6.1. For a rectangular parallelepiped (i.e. a ‘brick’ or ‘block’ shape) the areas S1 and S2 are easy to calculate: S1 = 0.12 x 0.4 = 0.024 m2, and S2 = 0.12 x 0.6 = 0.048 m2. Hence:
3
6 S/
S u
3
6 S/
S u
We can now use Eq. 6.25 to determine Ef:
(I
%L %L 3 3 3 3 %L %L
u u
The Wake the only emission we want to leave behind
.QYURGGF'PIKPGU/GFKWOURGGF'PIKPGU6WTDQEJCTIGTU2TQRGNNGTU2TQRWNUKQP2CEMCIGU2TKOG5GTX 6JGFGUKIPQHGEQHTKGPFN[OCTKPGRQYGTCPFRTQRWNUKQPUQNWVKQPUKUETWEKCNHQT/#0&KGUGN6WTDQ 2QYGTEQORGVGPEKGUCTGQHHGTGFYKVJVJGYQTNFoUNCTIGUVGPIKPGRTQITCOOGsJCXKPIQWVRWVUURCPPKPI HTQOVQM9RGTGPIKPG)GVWRHTQPV (KPFQWVOQTGCVYYYOCPFKGUGNVWTDQEQO
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Chilling and Freezing
Next we calculate ξ3 and ξ4 from Eqs. 6.29 and 6.30:
[
UX & S X 7f 7 I '+
[
U I & S I 7 I 7L '+
u u u
u u u
From which we can calculate ξ1 and ξ2 from Eqs. 6.27 and 6.28:
[
[ [[
[ [
Finally we calculate tf from Eq. 6.26:
WW
/'+ [ [ %L ( I K 7f 7 I
u u u u u u
u V | KRXUV
6.4
Summary of Chapter 6
In order to design suitable refrigerated facilities, one needs to know the chilling or freezing times of the product; this will then allow for the calculation of heat loads, and inally will allow the necessary refrigeration capacity to be determined. As irst approximations, relatively simple, semi-empirical calculation procedures may be employed, provided the necessary input data (e.g. thermal properties, heat transfer coeicients, initial, target, and cooling medium temperatures) are available. For greater accuracy, numerical methods may be employed, and commercial sotware packages especially for this purpose have been developed.
6.5
Further Reading
ASHRAE Handbook: Refrigeration, American Society of Heating, Refrigeration and Air Conditioning Engineers, Atlanta, 2010 Hayakawa, K, Villalobos, G, Formulas for estimating Smith et al. parameters to determine the mass average temperature of irregularly shaped bodies, Journal of Food Process Engineering, 11, 237–256, 1989 Rahman, MS, Food Properties Handbook 2nd Ed., CRC Press, Boca Raton, Florida, 2009
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Chilling and Freezing
Pham, QT, Cooling/Freezing/hawing Time and Heat Load, in: Sun, D-W, Advances in Food Refrigeration, Leatherhead Publishing, Surrey, 2001 Pham, QT, Trujillo FJ, Davey, LM, McPhail, N, Cooling curves for the preliminary design of beef chillers, International Journal of Refrigeration, 32. 1944–1953, 2009
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7 Food Refrigeration Most people probably associate the term ‘refrigeration’ with the domestic refrigerator, which is reliable and simple to use, and is bought as a single unit containing both the chiller and the freezer. Industrially and commercially the situation is quite diferent. Not only will chillers and freezers oten be entirely separate units, but the components of a refrigerator (compressor, condenser, expansion device and evaporator) will not necessarily be purchased at the same time, or necessarily from the same supplier. A single compressor may service multiple evaporators in diferent refrigerated environments; or alternatively multiple compressors may be required for a single chiller or freezer, if it has a large heat load. In fact, for a large refrigerated facility such as may be found at abattoirs there may be a number of compressors, condensers, expansions and evaporators all connected in a network, so that varying cooling capacity may be applied to diferent rooms as required. On the industrial scale it is convenient to separate refrigeration applications into four categories: cooling a product to above its initial freezing temperature is known as ‘chilling’; maintaining it at temperatures above the initial freezing point, is known as ‘cool storage’; cooling a product below its initial freezing temperature is known as ‘freezing’; maintaining its temperature below its initial freezing temperate is known as ‘cold storage’. While these deinitions are not always used, they are useful to bear in mind. In this chapter, ‘refrigerated environment’ is used as a general term to cover all four of these classes.
7.1
The Domestic Refrigerator
Every reader of this book will be familiar with the ubiquitous domestic refrigerator. Modern ‘fridges’ are simple to use, durable and reliable. he most widely used model is the upright fridge/freezer, although units which only serve as ‘fridges’ or only as freezers are also common. he domestic fridge is almost invariably based on the vapour compression cycle; however, for a fridge/freezer unit the basic design is slightly diferent to the standard vapour compression cycle illustrated schematically in Figure 2.7c. his is because in order for the two compartments to be maintained at diferent temperatures (the fridge compartment typically at 4 °C and the freezer compartment typically at -18 °C), the expansion process needs to be separated into two stages. However, since typically only a single compressor is employed, the energy savings of multi-stage compression (as described in Chapter 2) are not possible. A schematic of the domestic refrigerator components is shown in Figure 7.1a with the corresponding PH diagram in Figure 7.1b.
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Figure 7.1a: Schematic of the essential components of the domestic fridge/freezer
Figure 7.1b: PH diagram for an ideal domestic fridge/freezer cycle
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Figure 7.1a shows the refrigerant passing through the fridge evaporator and freezer evaporator in series – an alternative, parallel arrangement is also possible. Note that the expansion valve is sometimes called a ‘metering device’ since it can be used to control the low of refrigerant (although its essential function is to reduce the pressure of the refrigerant). With variable-speed compressors which may be used to control the low of refrigerant becoming more common, many modern domestic refrigerators achieve the expansion simply be crimping a restriction (throttle) into the refrigerant line – with no actual valve required.
7.2
The Cold Chain
Most food will go through several diferent stages of chilling/freezing and cool/cold storage between the time it is harvested and the time it is consumed. To illustrate just how signiicant a role refrigeration plays in keeping us fed, consider frozen beef being exported from New Zealand to Europe. Immediately ater it has been slaughtered and ‘dressed’ (i.e. had the head, hide, ofal, tail etc. removed) a side of beef will be placed in a carcass chiller for a period of more than 24 hours. Following the chilling process it will be separated into diferent cuts in a ‘boning room’ maintained at about 10 °C and packed into cartons. hese cartons will then be placed in a blast freezer before being stored frozen, until they are ready to be transported. When they are ready to be transported they will probably be loaded into refrigerated (‘reefer’) containers and placed on either a road or rail truck and taken to a seaport. At the port they will be loaded onto a ship which will sail to Europe, a journey that will take several weeks to complete. Ater being unloaded at the destination port, the beef will most likely be taken to a cold storage facility at the retailer’s warehouse. At some point the meat will be placed in a refrigerated retail display cabinet (e.g. at a supermarket) for sale. Once purchased, it will most likely spend some time in the customer’s domestic refrigerator.
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he journey of the beef from the abattoir to the customer’s home is referred to as the Cold Chain, since refrigeration plays such an important role at every stage of its journey. Some countries are net importers of food, meaning they rely on food from other countries to keep their population fed (e.g. Lebanon imports more than 80% of its food!). A robust, efective Cold Chain is obviously vital for feeding the ever-increasing global population. his means that at each stage (each ‘link’ in the ‘chain’) the product’s ‘temperature integrity’ must be maintained (i.e. its temperature must be held between certain limits). Failure in the cold chain is oten due to poor handling and logistics, and can be responsible for loss of product during transportation, rejection of the product by the customer or retailer, or else food poisoning if it is unhygienic when consumed.
7.3
Typical examples of refrigerated facilities
Figure 7.2 shows a schematic of a typical, multi-purpose freezing facility. he facility is divided into cold stores accessed by a central air-lock passageway. he stores may each be maintained at diferent temperatures, while the air-lock will typically be the closest to ambient in temperature. For large facilities the stores will be accessible by forklit, and in some cases small trucks. Oten a truck will be able to enter the air-lock at least, in order that it may be loaded under cool conditions.
Figure 7.2: Schematic of a cold-store, including blast freezers
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he access-ways in the facility need to be designed to minimize heat and moisture ingress to the stores. his may be achieved in a number of ways, but the most common ones include roller doors, strip curtains, and air curtains (i.e. jets of air that are sent down from vents above the doorways to provide positive pressure against the air within the store) or a combination of these. If no signiicant traic into or out of a store is expected for signiicant periods, then a properly insulated door will be pulled across the access-way to achieve a near air-tight seal. In one corner of two of the stores in Figure 7.2 is an air blast freezer. A schematic of a blast-freezer is shown in Figure 7.3.
Figure 7.3: Schematic of a blast freezer
Product, which typically has been pre-packaged, is placed onto racks which allow space for air-low between the product boxes. he evaporator fans generate high velocities (>10 m s-1) to achieve high rates of freezing. Once a batch has been frozen, it will be removed and placed in the storage area outside the blast freezer, and a new batch will be placed in the blast freezer. In addition to the generic cold-store and blast-freezer complex shown in Figure 7.2, there are some more specialised refrigeration facilities. A carcass chiller (illustrated schematically in Figure 7.4) is essentially a large room with a relatively low ceiling in which whole lamb carcasses, or pork or beef sides are hung on rails. Most carcass chillers will have some type of arrangement to ensure air is distributed throughout the chiller to minimise variation in chilling rates in diferent regions of the room. Some modern carcass chillers even use water spray, if permitted by regulatory bodies, to increase chilling rates and minimise weight loss. Carcasses are usually cooled for several hours before either being transported for sale whole, or more commonly packaged as individual cuts, oten with the removal of signiicant amounts of fat and bone. he rooms where the carcasses are cut (sometimes referred to as ‘boning rooms’) also need to be maintained at temperatures well-below ambient (e.g. 10 °C). Download free eBooks at bookboon.com
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Figure 7.4: Schematic of a carcass chiller
Fruit and vegetable cool-stores are oten itted with equipment to control the composition of the gas in the room, in order to restrict the rate of ripening and/or reduce the moisture loss during storage. Controlled Atmosphere (CA) storage refers to the storage facilities in which the amounts of oxygen, nitrogen and carbon dioxide or monitored and controlled, oten with oxygen levels lower than found in air. Modiied Atmosphere (MA) storage (oten part of the packaging) refers to environments in which the amount of oxygen is greatly reduced, or essentially removed altogether, and has been found to extend shelf-life signiicantly.
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Most ishing vessels have on-board cold-storage facilities, since they may be away from port for weeks at a time. Some species are simply packed whole in ice in insulated rooms below deck, while other species may be partially ‘dressed’ (e.g. have their heads, guts and tails removed) on deck before being packed into boxes, frozen in a plate-freezer, and placed in a cold-store.
7.4
Design Considerations
Regardless of the speciic design of the chiller, freezer, cool- or cold-store, there are some general design considerations that apply. 7.4.1
Capacity and Temperature
Probably the irst decisions that need to be made are what quantity of product is expected to be cooled/ stored and at what temperature. For the chilling and freezing processes (as opposed to cool and cold storage), the initial temperature is also important. he quantity and temperatures of the product will determine the required capacity of the refrigeration (in terms of kW), using techniques similar to ones described in Chapter 6. In addition to the heat load from the product, a number of other sources can contribute to the total heat load, depending on the type of refrigerated environment: - Heat iniltration through walls, loor, ceiling, pillars, beams etc. (should be minimised by good insulation) - Heat from warm, humid air coming in through doors or other access-ways (see Section 7.4.3) - Heat from evaporator fans circulating the air in the refrigerated environment - Heat from lights - Heat of respiration (not only from humans present, but also from some products, fruit and vegetables in particular) - Heat from forklit trucks or other vehicles used to transfer product in - Heat from the defrost cycle (see Section 7.4.3) he relative magnitudes of each component within the total heat load will vary widely between diferent refrigerated environments. Many of the components of the heat load may be determined using simple variations of Eq. 3.11. Once the total heat load has been estimated, and an appropriate design safety factor has been applied, the selection of the most efective compressor and refrigerant pairing (‘efective’ here being meant to include both energy eiciency and cost) may be made.
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7.4.2
Food Refrigeration
Air movement
he cooling medium for most refrigerated facilities is air. Typically the evaporators of the refrigeration system are located in one part of the refrigerated environment with fans being relied upon for circulating the air. One problem that can arise is that of ‘short-circuiting’, where cold air exiting the evaporator(s) is sucked back around to the inlet, without passing over most of the product. his will lead to relatively warm regions (‘hotspots’), resulting in signiicantly reduced cooling times, or product not reaching the required temperature at all. It may not be suicient simply for air to be well-distributed in the head space above the product and in aisle spaces; signiicant air-low through the product stacks may also be required in order to achieve not only the desired rate of cooling, but also uniform rates of cooling between product stacks in diferent parts of the refrigerated environment. In addition to the evaporator fans, which are standard, air movement can be aided by difusers, vanes and ducting that can distribute the air optimally, at the expense of higher pressure drops needing to be overcome by the fans. (Note that not all chillers and freezers use air, some rely on liquids such as water or an ‘anti-freeze’ solution, or by direct physical contact, in the case of plate freezers. However, most cool/cold stores use air). 7.4.3
Control of moisture
It is almost impossible to prevent moisture entering refrigerated environments where it increases the cooling load (due its latent heat of evaporation), reduces the efectiveness of the evaporator (by causing frost and/or mould build-up on the heat exchange surface) and can also be a hazard, particularly in freezers and cold stores, where ice can build up on the loor and potentially result in slips. Moisture may enter the refrigerated environment as humidity in the air that accompanies staf and product when they enter, or from the product itself as it cools (e.g. carcass chillers and fruit stores in which the product can release signiicant quantities of moisture). Most chillers and cool-stores will have humidity control, since humidity is oten a signiicant factor in determining the shelf-life of chilled products. Almost all evaporators will have some sort of defrost-mechanism, which typically involves heating the evaporator surface to melt any ice that has built-up (note that even chillers and cool-stores may have ice build-up, since the evaporator temperature may have to be below 0 °C, in order to maintain air temperatures of 0 to 4 °C). he heating of the evaporator surface may either be achieved externally, or by allowing some of the refrigerant exiting the compressor to bypass the condenser and expansion, and enter the evaporator as a hot vapour. he defrost cycle is an extra heat load, but is compensated for by the improved performance of the evaporator.
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Measures are also taken to restrict the quantity of warm, humid air entering the refrigerated environment through the use of strip curtains and air curtains, and by management of the number of entries and exits to/from the refrigerated environment. 7.4.4
Insulation
Efective insulation is critical for the eiciency of cool/cold stores. Ideally insulation is incorporated within the structural elements of the building when the facility is built, since this tends to result in the most durable arrangement. Spray-on, foam insulation may be used if an existing building has been converted to a cool/cold store. It is important to recognise that it is not only walls and doors that need to be insulated, but also ceilings and, for freezers and cold stores in particular, loors. Insulation should not only provide a barrier to heat transfer, it should also be efective as a moisture barrier. his is not only to prevent moisture ingress from outside, but also to prevent moisture from within the store permeating the insulating material, which can signiicantly reduce its efectiveness. Particular care is needed to ensure moisture barriers are maintained at joins between walls, loors and ceilings. Floor insulation is highly recommended for freezers and cold stores, to prevent ice forming in the soil below, which may then crack concrete loors as it expands (a phenomenon known as ‘frost heave’). he alternative would be to heat the soil underneath to prevent it from freezing, but would be an added running cost, not only from the direct heating cost, but also the added heat load from iniltration through the loor to the store.
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7.4.5
Food Refrigeration
Access-ways and traic
Access-ways (mainly doors, but possibly hatches and windows) in cool/cold stores need to be practical in the sense that they need to be in convenient positions and large enough to allow stacks of product and its transportation (e.g. forklit trucks) to pass through. However, the larger the access-way the greater the amount of warm, moist air that can iniltrate the refrigerated environment, and if the access-way is too close to the evaporator fans, then cold air can be blown out at the same time that warm, moist air is sucked in. Strip curtains, air curtains and roller doors can help minimise these losses, but clearly optimisation is required to balance the potentially conlicting requirements of practicality and energy eiciency. Smart scheduling of the loading and unloading of refrigerated environments can also be used to minimise the number of accesses, and hence the quantities of cold air that is lost and warm, moist air that replaces it. Cool/cold stores are oten large enough to have forklit trucks driving around in them, and a storage facility may have a central air-lock (see Figure 7.2) that is large enough to contain a transportation truck, so that product can be loaded under cool conditions, out of direct sunlight. Where possible, electric vehicles should be used since they produce much less heat than petroleum-fuelled vehicles, and no moisture vapour exhaust. Electric forklits are very common; however, the majority of transport vehicles are diesel-fuelled. Clearly, if a diesel truck is inside a store it should not be allowed to idle while it is being loaded, as oten tends to be the case when trucks are loaded outside a store. 7.4.6
Controlled and modiied atmospheres
he design of controlled and modiied atmosphere stores requires extra care and consideration, since they will need to be sealed suiciently to prevent signiicant ingress and egress of gases. he number of accesses in a controlled atmosphere store should be minimal; in fact the ideal is for a batch of product to be loaded into the store, the store to be sealed, and then let until the required storage time has elapsed, at which point the entire batch is unloaded. However, this will not always be possible for logistical reasons.
7.5
Refrigerated transport
Refrigerated transport vehicles may be thought of as special classes of cool/cold stores (and in some cases they also do some chilling and freezing). Road trucks, rail-trucks, ships and airplanes are all in use for transporting refrigerated food. Some vehicles only have thermal insulation and rely on the thermal mass of the product to maintain temperature integrity; however, many have their own active refrigeration system. Reefer containers in particular have become popular, since they are modular and can be used with road, rail and sea transportation, simply by plugging them into a power source.
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Most of the general design principles described in Section 7.4 apply to refrigerated transport; however, there are obviously extra considerations that need to be made. For example, a reefer container, which must draw its power from an external source, either mains power at a warehouse or the truck/train/ship transporting it, needs to be plugged in manually at the start of each stage of its journey – simple human error, could mean that is not. For frozen product, occasional lapses can be tolerated but for chilled product such a mistake can spoil the contents of an entire container. Hence a reefer is more likely to experience power failure than a permanent refrigerated building with hard wired power. Also, refrigeration systems on transports experience far more vibration and mechanical shock than permanent structures, and hence are more exposed to failure by wear and tear. he logistics associated with refrigerated transport is also, perhaps, a more diicult exercise than managing a cool/cold store facility since tracking the location and monitoring temperatures of the product is conined to a much smaller space. Since there are typically a number of diferent parties involved in the cold chain of a particular product, it will not always be clear who is to blame if and when a failure occurs which results in the loss of product. Unsurprisingly there are frequent disputes between producer, transport companies, warehouse companies, port companies and retailers, many of which result in litigation. For this reason there has been, particularly in Developed Nations, greater eforts put into auditing the cold chain, using a variety of diferent methods to monitor the product’s temperature over time, and preferably to identify when a failure has occurred, and therefore who is culpable.
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Food products have diferent optimal transportation conditions – the most signiicant of which is the product temperature. Tables 7.1 to 7.3 show transportation conditions recommended by the International Institute of Refrigeration, for three diferent classes of chilled product.
Product
Recommended transportation temperature
Temperature range limits
Initial freezing temperature
Typical Shelf life
°C
°C
°C
(days)
Apples
0
-0.5 to +2
-1.5
varies between species
Apricot
-0.5
-0.5 to 1
-1.5
20
Avocado
7
4.5 to 13
-0.5
Bananas
12
12 to 13.5
-1
24
Cherry
-0.5
-1 to 0
-1.5
20
Grape
-0.5
-1 to +0.5
-1.5
50 to 100
Grapefruit
10
+4.5 to +16
-1
40
Plum
-0.5
-0.5 to +0.5
-1
20 to 35
Kiwifruit
-0.5
-0.5 to +0.6
-2
50 to 75
Lemon
10
+5 to +16
-1.5
80
Mango
10
9 to 12
Nectarine
-0.5
-0.5 to +0.5
-1
Orange
4.5
+3 to +7
-1
40 to 50
Papaya
7
4 to 12
-1
14 to 21
Peach
-0.5
-0.5 to +1
-1.5
30
Pear
-0.5
-1 to +0.5
-1.5
60 to 150
Pineapple
8.5
+7 to +10
-1
30
Watermelon
10
4.5 to 10
Table 7.1: Recommended transportation conditions for selected fruits
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Product
Recommended transportation temperature
Temperature range limits
Initial freezing temperature
Typical Shelf life
°C
°C
°C
(days)
Asparagus
0
0 to 1
-0.5
20
Aubergine
7
7 to 10
-0.5
14
Beans (French)
0
0 to 7
-0.5
20
Beetroot
0
0 to 1
-0.5
60 to 90
Broccoli
0
0 to 1
-0.5
10
Brussels sprouts
0
0 to 1
-0.5
30
Cabbage
0
0 to 1
-0.5
20
Carrots
0
-0.5 to 0.5
-0.5
70
Caulilower
0
0 to 1
-0.5
30
Celery
0
0 to 1
-0.3
60 to 90
Endive
0
0 to 1
-0.5
14 to 20
Cucumber
7
7 to 10
-0.3
14
Garlic
0
0 to 1
-0.5
150
Ginger
12
10 to 13
150
Leeks
0
0 to 1
-0.5
60
Lettuce (iceberg)
0
0 to 1
-0.5
40
Onions
0
0 to 1
-0.5
30 to 120
Peas (in pod)
0
0 to 1
-0.5
7 t0 20
Peppers
7
7 to 10
-0.5
20
Potatoes
7
4.5 to 10
-0.5
60 to 150
Pumpkin
10
10 to 13
-0.5
60 to 90
Rhubarb
0
0 to 1
-0.5
15 to 30
Sweet potato
13
13 to 16
-1
120
Tomato (green)
13
10 to 16
-0.5
20
Table 7.2: Recommended transportation conditions for selected vegetables
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Product
Recommended transportation temperature
Temperature range limits
Initial freezing temperature
Shelf life
°C
°C
°C
(days)
Typical
Bacon
-1
-2 to 4
Beef (chilled, quarters)
-1.5
-0.5 to 1
-1.7
20
Beef (chilled, packed)
-1.5
-0.5 to 2
-1.7
70
Butter
0
-1 to 4.5
30
Cheese
2
0 to 10
varies with variety
Cream
0
-1 to 0.5
-2.2
10
Eggs
0
-1 to 0.6
-0.6
180
Seafood
-0.5
-2 to 4.4
-2.2
14 to 20
Venison
0
-1.5 to 0
14
Ham
-0.5
-1.5 to 0.5
21
Lamb (chilled, whole)
-1.5
-1.5 to 0
-1.9
30
Lamb (chilled, packed)
-1.5
-1.5 to 1
-1.9
70
Lard
0
-1.5 to 4.5
180
Margarine
0
-1.5 to 0.5
180
Milk (pasteurised
0
-0.5 to 1
-0.6
14
Pork (unsalted)
-1.5
-1.5 to 0
-2.2
14
Pork (salted)
4.5
-1 to 7
120
Poultry
-1
-1.5 to 1.5
-2.8
14
Table 7.3: Recommended transportation conditions for selected protein foods
7.6
Summary of Chapter 7
he ‘Cold Chain’ is the term given to the various refrigeration stages that a food (or pharmaceutical) product experiences between harvest/production and consumption. he term ‘chain’ is appropriate since the food may be spoiled by lack of temperature integrity (‘failure’) at any stage (‘link’) in the chain. Careful design and operation of refrigerated environments and good logistical management are required in order to maintain temperature integrity throughout the chain, thereby satisfying producer, retailer and customer, and, more importantly, allowing for a steady supply of food year round.
7.7
Further Reading
ASHRAE Handbook: Refrigeration, American Society of Heating, Refrigeration and Air Conditioning Engineers, Atlanta, 2010 Heap, R (Ed.), Guide to Refrigerated Transport 2nd Edition, International Institute of Refrigeration, Paris, 2010
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Hundy, GF, Trott, AR & Welch, TC, Refrigeration and Air Conditioning, 4th Ed., Butterworth Heinemann, Oxford, 2008 Pham, QT, Trujillo FJ, Davey, LM, McPhail, N, Cooling curves for the preliminary design of beef chillers, International Journal of Refrigeration, 32. 1944–1953, 2009 Rahman, MS, Food Properties Handbook 2nd Ed., CRC Press, Boca Raton, Florida, 2009
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Air Conditioning
8 Air Conditioning ‘Air conditioning’ is the term used to describe the supply of comfortable, healthy air to the interior of building. Oten this requires the air to be cooled (i.e. refrigeration), but humidity regulation, air movement (ventilation), and dust and odour removal are also important. Comfortable room temperatures tend to be in the range of 19 °C to 25 °C, comfortable humidity levels tend to be in the range of 60 to 80% (at comfortable room temperatures), and air movement up to 0.25 m s-1 for ventilation is considered comfortable. However, since this is a book about refrigeration, this chapter will focus briely on the refrigeration aspect of air conditioning.
8.1
Air-conditioning Cooling Load Calculations
Air-conditioning for human comfort has slightly diferent aims compared to food refrigeration, in that we are not trying to reduce the core temperature of the human body. Instead we are concerned with removing the heat generated by the human body, by lighting and appliances that give of heat as a waste product, and also to cool fresh air from outside for ventilation purposes. For this reason, steady-state models similar to the ones discussed in Chapter 3 would be suicient for estimating cooling loads. 8.1.1
Heat load categories
Heat loads for air-conditioning can come from a variety of sources, which may be divided into two categories: internal heat loads and external heat loads. Internal heat loads include: - Humans – a person involved in normal indoor activity will produce between 100 and 600 W depending on their age, size and speciic activity (see Table 8.1). Hence a room illed with a large number of people can be a signiicant heat load, measuring in the region of several kilowatts. - Lighting – each light gives of a certain wattage and individual bulbs can be in the range of 100 W. - Appliances/machines – large televisions, domestic refrigerators, washing machines, computers all give of heat while in use. Any appliance that uses electricity will produce heat as a waste product.
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External heat loads include: - Solar loads – the biggest solar gain is by sunlight shining through transparent surfaces such as windows. Sunlight heating walls and roofs can also add signiicantly to the heat load on a room, particularly if there is little thermal cladding. Estimating solar loads accurately is more complex than for internal gains, however, several sources (including those listed at the end of the chapter) provide relatively simple guides - Hot winds – although typically much less of a factor than solar loads can be signiicant if there is poor thermal cladding on the building. Of course strong winds which are lower in temperature than the external surface temperature of the building will actually reduce heat loads Activity
Heat Load
W
Sleeping
70
Seated, still
100
Standing
150
Walking at 3 km/h
300
Oice work
150
Retail work
180
Industrial
300–600
Table 8.1: Typical values of heat produced by human activity (adapted from Stoecker and Jones)
8.1.2
Air conditioning heat load estimation procedure
he following procedure is adapted from the recommendations of Stoecker and Jones (listed at the end of the chapter): 1. Determine the design-basis external air temperature and humidity (i.e. the climate in the geographical region where the building is located). Typically this means using a conservative value, i.e. for cooling, the design might be based on the 98th percentile temperature (i.e. the value which the actual temperature is lower than for 98% of the time) 2. Select the desired air temperature and humidity within the building (e.g. 22 °C, 60 % humidity) 3. For each room being considered estimate the temperature in any adjacent rooms 4. Estimate the overall heat transfer coeicients (U) within each room 5. Estimate the rate of iniltration of air (including active ventilation) into the room 6. Determine the latitude, orientation, external shading that will afect solar heat-load calculations 7. Determine the thermal properties of the building and insulation materials and the heat transfer coeicients within the rooms
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Air Conditioning
8. Calculate the rate of heat gain into the room from external sources 9. Estimate the maximum number of people likely to be within each room, and their most active occupation 10. Determine the amount of lighting and the power consumption of appliances/machines that will be within each room 11. Sum the internal and external heat loads to estimate the required cooling capacity Many of the steps above require location-speciic and material speciic data. Sources such as the ASHRAE Handbook of Fundamentals, contain much of this required data, particularly for buildings located within the United States. Once the required input data have been obtained most of the individual calculation steps are relatively straightforward (oten being simple variations of Eq. 3.11), provided the procedures are followed correctly. he following example illustrates the types of calculation involved. Example 8.1: Estimate the internal heat generation that could be expected for an oice which will be occupied by 4 to 8 people, four lap-top computers, a small fridge and 10 luorescent tube lights in the ceiling.
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Solution: Indicative values for the power consumption of appliances are relatively simple to obtain, and is oten indicated on the appliance itself (or from manufacturer’s data on the internet). A small fridge will draw about 200 W, while lap-top computers might draw 50 W each. Each tube light may be assumed to draw 30 W (including the ballast). Since up to eight people may be expected to occupy the oice we should use that number along with the data in Table 8.1 to estimate the heat load. Hence:
4 DSSOLDQFHV u u : 4 OLJKWLQJ u : 4 RFFXSDQWV u : ?4 WRWDO
4 DSSOLDQFHV 4 OLJKWLQJ 4 RFFXSDQWV :
Note that in this example the largest internal heat load is from the occupants. he inal value would be more meaningful if it could also be expressed on a per unit volume (of the room) basis, or at least on a per loor-area basis, since that will give an idea of the load density, as well as the total load.
8.2
Domestic air-conditioning
Once the design conditions and cooling load have been determined, an appropriate air-conditioner may be selected. For most domestic applications, air-conditioners are based on the vapour-compression cycle, although evaporative coolers are popular in hot, dry climates (see Chapter 5). he operation principle of the air-conditioner is identical to that of the food refrigerator, as outlined in Chapter 2, with the same four essential components (namely the compressor, condenser, expander and evaporator). he main diference between the air-conditioner and food refrigerator is in its mechanical design (obviously, it does not have an enclosed product space). Even for a domestic unit, it may not be a single physically contiguous unit (by contrast with the domestic refrigerator). Perhaps the most common design option in current use in a number of countries outside the tropics is the split, invertible heat pump, which is illustrated schematically in Figure 8.1.
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Air Conditioning
Figure 8.1: Invertible domestic heat pump/air conditioner; a) air-conditioning (cooling) coniguration, b) heat pumping (heating) coniguration
A simple 4-way value is employed to convert the heat pump (in which the heat exchanger inside the home is the high temperature condenser) into an air conditioner (in which the heat exchanger inside is the low-temperature evaporator).
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8.3
Air Conditioning
Large-scale air-conditioning
Simple ‘package’ heat pump/air conditioners may be most practical and economical for the domestic setting, but for larger scales a more integrated approach will oten be more efective (although large buildings sometimes have numerous individual domestic-scale air conditioners). In a large building there may be several heat sources and several heat sinks. In this case individual heat pumps can be combined in a network which also contains Air Handling Units (AHUs). Water is oten used as a secondary refrigerant to transport heat away from one space to another. In recent times data centres (i.e. rooms that house ile servers and other computing equipment) have become a special air-conditioning application. he heat generation density (i.e. watts generated per square metre of loor area) can be signiicantly higher than for a room occupied mainly by people. In cold climates, large volumetric low-rates of air may be suicient to keep the centre at the required temperature; however, water will need to be used as a medium for carrying the heat, due to the high heat generation density. Where possible evaporative cooling will be employed, but if the long-term wet-bulb temperature of the ambient air is not suiciently low (i.e. warm, humid climates) then air conditioning, or refrigeration of the cooling water will be required.
360° thinking
.
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8.4
Air Conditioning
Summary of Chapter 8
‘Air conditioning’ refers to the process of achieving and maintaining air within certain constraints of temperature, humidity, and freshness. From a temperature management perspective, it is an identical process to refrigeration, usually employing the vapour-compression cycle (with the notable exception of evaporative coolers in hot, dry climates). Many air conditioners can be used to provide both cooling and heating (heat pumping) by redirecting the low of refrigerant within the system.
8.5
Further Reading
ASHRAE Handbook: Refrigeration, American Society of Heating, Refrigeration and Air Conditioning Engineers, Atlanta, 2010 ASHRAE Handbook: Fundamentals, American Society of Heating, Refrigeration and Air Conditioning Engineers, Atlanta, 2009 Çengel, YA & Boles, MA, hermodynamics: An Engineering Approach, 7th Ed., McGraw Hill, New York, 2011 Çengel, YA & Ghajar, AJ, Heat and Mass Transfer: fundamentals and applications, 4th Ed., McGraw Hill, New York, 2011 Hundy, GF, Trott, AR & Welch, TC, Refrigeration and Air Conditioning, 4th Ed., Butterworth Heinemann, Oxford, 2008 Stoecker, WF & Jones, JW, Refrigeration and Air Conditioning, 2nd Ed., McGraw Hill, New York, 1986 Rahman, MS, Food Properties Handbook 2nd Ed., CRC Press, Boca Raton, Florida, 2009
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Cryogenics and Gas Liquefaction
9 Cryogenics and Gas Liquefaction 9.1
Cryogenics
he term ‘cryogenic’ refers to low temperatures, and while there is no universally agreed upon threshold deining the start of the cryogenic temperature range, it is in the vicinity of -100 °C to -150 °C. Cryogenics inds applications in the following ields: - Transportation of natural gas - Electricity transmission (the lower the temperature the lower the transmission losses) - Superconductivity research and modern physics (e.g. in CERN’s Large Hadron Collider) - Cryo-surgery - MRI and other analytical tools - Rocket propulsion (liquid hydrogen as the fuel, liquid oxygen as the oxidiser) - Long-term storage of biological media (e.g. blood and sperm) - Industrial applications he search for the lowest achievable temperature is a ield of research in itself, as workers strive to get closer and closer to absolute zero. Cryogenic refrigeration is most commonly achieved by allowing a liqueied gas to evaporate to the atmosphere. his is a very simple method of maintaining a steady, low temperature. Table 9.1 shows the normal boiling points (i.e. boiling points at atmospheric pressure) of a selection of gases.
K
°C
He
4.22
-268.93
H2
20.28
-252.87
O2
54.36
-218.79
N2
77.36
-195.79
CH4
90.7
-182.45
C2H6
184.6
-88.55
C3H8
231
-42.15
Table 9.1: Normal boiling points of some gases
Liquid nitrogen is perhaps the most widely used cryogenic refrigerant, while liquid helium achieves the lowest temperatures. Since we do not ind the gases listed in Table 9.2 occurring naturally in the pure, liquid state, clearly there needs to be some way of producing them.
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9.2
Cryogenics and Gas Liquefaction
Gas Liquefaction
In order to liquefy a gas using the standard vapour compression cycle, we would need a refrigerant with a very low evaporation temperature – lower than the boiling point of the gas we are trying to liquefy. Instead we essentially use the gas we are trying to liquefy as the refrigerant, and use the cooling efect that accompanies the expansion of gases under most (but not all!) conditions. Figure 9.1a shows a schematic of a gas liquefaction process, and Figure 9.1b shows the cycle on a TS diagram.
ϭϬϬϬ
7
ϭϬϬ
ϭϬ
ϭ
Ϭ͘ϭ
Ϭ͘Ϭϭ Ϭ͘ϱ
D
ϭ
ϭ͘ϱ
Ϯ
Ϯ͘ϱ
ϯV
E
Figure 9.1: Gas liquefaction process, a) schematic diagram, b) TS diagram
To achieve the lowest temperature from an expansion process, we want the gas to be at as high a pressure as possible, and as low a temperature as possible at the inlet to the valve or throttle. Consider a gas at ambient conditions before it enters the compressor (State 1 in igure 9.1). If we compress it isentropically its temperature will increase (State 2). We should cool it isobarically down to as low a temperature as possible, irstly using some external cooling (State 3), but also relying on the fraction of gas that is not liqueied by the expansion process (State 4). Once we have cooled the gas as much as possible it is expanded through a throttle or valve into a lash drum (State 5) where a fraction of the gas is liqueied (State 9) and is the product, while the un-liqueied gas (State 6) is returned to the compressor via the regenerator where it transfers heat to the compressed gas which is being cooled prior to expansion. Ater the regenerator (State 7) the gas is mixed with make-up feed gas (State 8) before the cycle is repeated. Referring to the TS diagram (Figure 9.1b), the closer State 5 is to State 9, the greater the fraction of liquid that is produced, and hence the more eicient the process is (on a mass basis). he work required to get the gas from State 1 to State 3 may be reduced signiicantly by using multi-stage compression. We could also potentially recover some work by expanding the gas through a turbine down to the start of the two-phase region, followed by expansion through a throttle for the remainder.
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Cryogenics and Gas Liquefaction
he liquefaction process is generally energy intensive, due to the large work of compression that is required as well as the need for external cooling, and hence cryogenic refrigeration tends to be very expensive (typically an order of magnitude more expensive than conventional vapour-compression refrigeration).
9.3
Summary of Chapter 9
Cryogenics refers to the study, production and application of low temperature. Simple cryogenic refrigerators operate by allowing a liqueied gas to evaporate at atmospheric pressure. Gases are liqueied by a process similar to the vapour compression cycle; however, the gas itself is essentially the working luid.
9.4
Further Reading
ASHRAE Handbook: Refrigeration, American Society of Heating, Refrigeration and Air Conditioning Engineers, Atlanta, GA, 2010 Çengel, YA & Boles, MA, hermodynamics: An Engineering Approach, 7th Ed., McGraw Hill, New York, 2011 Smith, JM, van Ness, HC & Abbott, MM, Introduction to Chemical Engineering hermodynamics, 7th Ed., McGraw Hill, New York, 2005
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List of Symbols
10 List of Symbols: a
cooling curve intercept (Eq. 6.2)
(m²)
A
area
(m²)
b
cooling curve slope (Eq. 6.2)
(s-1)
Bi
Biot Number deined by Eq. 3.22
C
number of components in a system
Cp
speciic heat capacity at constant pressure
(J kg-1 K-1)
Cv
speciic heat capacity at constant volume
(J kg-1 K-1)
E
equivalent heat transfer dimensionality
f
cooling curve time constant (Eq. 6.5)
F
number of degrees of freedom
Fo
Fourier Number deined by Eq. 3.21
G
shape factor deined in Chapter 6
h
heat transfer coeicient
(W m-2 k-1)
h
speciic enthalpy
(J kg-1)
H
enthalpy
(J)
j
cooling curve intercept (Eq. 6.5)
k
thermal conductivity
(W m-1 k-1)
L
length
(m)
L
shortest distance between centre and surface
(m)
N
number of phases in a system
P
pressure
P1,P2
shape factors deined in Chapter 6
Q
heat
(J)
Q
heat low
(W)
r
radial dimension
(m)
R
radius
(m)
R
universal gas constant
8.314 (J mol-1 K-1)
s
speciic entropy
(J kg-1 K-1)
S
entropy
(J K-1)
S1,S2
shape factors deined in Chapter 6
T
temperature
(°C or K)
U
internal energy
(J or J kg-1)
(s)
(Pa)
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List of Symbols
(m3)
V
volume
x,y,z
Cartesian coordinates
q
l
dimensionless temperature change deined by Eq. 3.20
y
density
x1, x2, x3, x4,
Function deined for a sphere by Eq. 3.25
r
function of Bi, deined for a sphere by Eq. 3.23
z
Function deined for a sphere by Eq. 3.24
(kg m-3)
intermediate variables deined by Eqs. 6.27 to 6.30
Subscripts 0
initial state
C
cold heat transfer process
f
frozen state
H
hot heat transfer process
i
inside/inlet
n
index of ininite series in Eq. 3.20
Net
net quantity
r
radial direction
rev
thermodynamically reversible process
s
surface
sph
sphere
o
outside/outlet
u
unfrozen state
x
x direction
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Appendix: Physical Properties of Refrigerant R134a
11 Appendix: Physical Properties of Refrigerant R134a Table A1: Properties of saturated R134a refrigerant (Generated from data available at webbook.nist.gov)
T
Psat
hf
hfg
hg
sf
sfg
sg
°C
MPa
kJ kg-1
kJ kg-1
kJ kg-1
kJ kg-1 K-1
kJ kg-1 K-1
kJ kg-1 K-1
-60
0.015906
123.46
237.85
361.31
0.68462
1.11638
1.801
-58
0.018091
125.81
236.77
362.58
0.69605
1.10045
1.7965
-56
0.020518
128.27
235.57
363.84
0.70741
1.08479
1.7922
-54
0.023206
130.73
234.38
365.11
0.71868
1.06952
1.7882
-52
0.026176
133.20
233.18
366.38
0.72988
1.05442
1.7843
-50
0.029451
135.67
231.98
367.65
0.74101
1.03959
1.7806
-48
0.033051
138.15
230.77
368.92
0.75207
1.02493
1.777
-46
0.037003
140.64
229.55
370.19
0.76305
1.01055
1.7736
-44
0.041329
143.14
228.32
371.46
0.77397
0.99643
1.7704
-42
0.046055
145.64
227.09
372.73
0.78482
0.98248
1.7673
-40
0.051209
148.14
225.86
374.00
0.79561
0.96869
1.7643
-38
0.056817
150.66
224.61
375.27
0.80633
0.95517
1.7615
-36
0.062908
153.18
223.36
376.54
0.81700
0.94180
1.7588
-34
0.069512
155.71
222.09
377.80
0.82760
0.92870
1.7563
-32
0.076658
158.25
220.81
379.06
0.83814
0.91566
1.7538
-30
0.084378
160.79
219.53
380.32
0.84863
0.90287
1.7515
-28
0.092703
163.34
218.23
381.57
0.85906
0.89014
1.7492
-26
0.101670
165.9
216.92
382.82
0.86943
0.87767
1.7471
-24
0.111300
168.47
215.6
384.07
0.87975
0.86535
1.7451
-22
0.12165
171.05
214.27
385.32
0.89002
0.85318
1.7432
-20
0.13273
173.64
212.91
386.55
0.90025
0.84105
1.7413
-18
0.14460
176.23
211.56
387.79
0.91042
0.82748
1.7379
-16
0.15728
178.83
210.19
389.02
0.92054
0.81736
1.7379
-14
0.17082
181.44
208.8
390.24
0.93062
0.80568
1.7363
-12
0.18524
184.07
207.39
391.46
0.94066
0.79414
1.7348
-10
0.20060
186.70
205.96
392.66
0.95065
0.78275
1.7334
-8
0.21693
189.34
204.53
393.87
0.9606
0.7714
1.732
-6
0.23428
191.99
203.07
395.06
0.97051
0.76019
1.7307
-4
0.25268
194.65
201.60
396.25
0.98037
0.74903
1.7294
-2
0.27217
197.32
200.11
397.43
0.99021
0.73799
1.7282
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Appendix: Physical Properties of Refrigerant R134a
Table A1: Properties of saturated R134a refrigerant – continued
T
Psat
hf
hfg
hg
sf
sfg
sg
°C
MPa
kJ kg-1
kJ kg-1
kJ kg-1
kJ kg-1 K-1
kJ kg-1 K-1
kJ kg-1 K-1
0
0.2928
200
198.6
398.6
1
0.7271
1.7271
2
0.31462
202.69
197.08
399.77
1.0098
0.7162
1.726
4
0.33766
205.4
195.52
400.92
1.0195
0.7055
1.725
6
0.36198
208.11
193.95
402.06
1.0292
0.6948
1.724
8
0.38761
210.84
192.36
403.2
1.0388
0.6842
1.723
10
0.41461
213.58
190.74
404.32
1.0485
0.6736
1.7221
12
0.44301
216.33
189.1
405.43
1.0581
0.6631
1.7212
14
0.47288
219.09
187.44
406.53
1.0677
0.6527
1.7204
16
0.50425
221.87
185.74
407.61
1.0772
0.6424
1.7196
18
0.53718
224.66
184.03
408.69
1.0867
0.6321
1.7188
20
0.57171
227.47
182.28
409.75
1.0962
0.6218
1.718
22
0.60789
230.29
180.5
410.79
1.1057
0.6116
1.7173
24
0.64578
233.12
178.7
411.82
1.1152
0.6014
1.7166
26
0.68453
235.97
176.87
412.84
1.1246
0.5913
1.7159
28
0.72688
238.84
175
413.84
1.1341
0.5811
1.7152
30
0.7702
241.72
173.1
414.82
1.1435
0.571
1.7145
32
0.81543
244.62
171.16
415.78
1.1529
0.5609
1.7138
34
0.86263
247.54
169.18
416.72
1.1623
0.5508
1.7131
36
0.91185
250.48
167.17
417.65
1.1717
0.5407
1.7124
38
0.96315
253.43
165.12
418.55
1.1811
0.5307
1.7118
40
1.0166
256.41
163.02
419.43
1.1905
0.5206
1.7111
42
1.0722
259.41
160.87
420.28
1.1999
0.5104
1.7103
44
1.1301
262.43
158.68
421.11
1.2092
0.5004
1.7096
46
1.1903
265.47
156.45
421.92
1.2186
0.4903
1.7089
48
1.2529
268.53
154.16
422.69
1.228
0.4801
1.7081
50
1.3179
271.62
151.82
423.44
1.2375
0.4697
1.7072
52
1.3854
274.74
149.41
424.15
1.2469
0.4595
1.7064
54
1.4555
277.89
146.94
424.83
1.2563
0.4492
1.7055
56
1.5282
281.06
144.41
425.47
1.2658
0.4387
1.7045
58
1.6036
284.27
141.8
426.07
1.2753
0.4282
1.7035
60
1.6818
287.5
139.13
426.63
1.2848
0.4176
1.7024
62
1.7628
290.78
136.36
427.14
1.2944
0.4069
1.7013
64
1.8467
294.09
133.52
427.61
1.304
0.396
1.7
66
1.9337
297.44
130.58
428.02
1.3137
0.385
1.6987
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Refrigeration: Theory And Applications
Appendix: Physical Properties of Refrigerant R134a
Table A1: Properties of saturated R134a refrigerant – continued
T
Psat
hf
hfg
hg
sf
sfg
sg
°C
MPa
kJ kg-1
kJ kg-1
kJ kg-1
kJ kg-1 K-1
kJ kg-1 K-1
kJ kg-1 K-1
68
2.0237
300.84
127.52
428.36
1.3234
0.3738
1.6972
70
2.1168
304.28
124.37
428.65
1.3332
0.3624
1.6956
72
2.2132
307.78
121.08
428.86
1.343
0.3509
1.6939
74
2.313
311.33
117.67
429
1.353
0.339
1.692
76
2.4161
314.94
114.1
429.04
1.3631
0.3268
1.6899
78
2.5228
318.63
110.35
428.98
1.3733
0.3143
1.6876
80
2.6332
322.39
106.42
428.81
1.3836
0.3014
1.685
82
2.7473
326.24
102.27
428.51
1.3942
0.2879
1.6821
84
2.8653
330.2
97.85
428.05
1.4049
0.274
1.6789
86
2.9874
334.28
93.14
427.42
1.4159
0.2593
1.6752
88
3.1136
338.51
88.04
426.55
1.4273
0.2437
1.671
90
3.2442
342.93
82.49
425.42
1.439
0.2272
1.6662
92
3.3793
347.59
76.33
423.92
1.4514
0.209
1.6604
94
3.5193
352.58
69.34
421.92
1.4645
0.1889
1.6534
96
3.6645
358.07
61.11
419.18
1.4789
0.1656
1.6445
98
3.8152
364.47
50.67
415.14
1.4957
0.1365
1.6322
100
3.9724
373.3
34.38
407.68
1.5188
0.0921
1.6109
101
4.0541
384.35
11.08
395.43
1.548
0.0296
1.5776
101.06
4.05928
389.89
0
389.89
1.5628
0
1.5628
Table A2: Properties of Superheated Refrigerant R134a (Generated from data available at webbook.nist.gov)
T
P = 0.1 MPa
P = 0.2 MPa
P = 0.3 MPa
P = 0.4 MPa
h
s
h
s
h
s
h
s
°C
kJ kg-1
kJ kg-1 K-1
kJ kg-1
kJ kg-1 K-1
kJ kg-1
kJ kg-1 K-1
kJ kg-1
kJ kg-1 K-1
-20
387.65
1.7677
-15
391.63
1.7833
-10
395.64
1.7986
392.68
1.7337
-5
399.67
1.8138
396.94
1.7497
0
403.73
1.8288
401.2
1.7654
5
407.82
1.8437
405.45
1.7808
402.88
1.7408
10
411.95
1.8584
409.73
1.7961
407.34
1.7567
404.72
1.7261
15
416.11
1.873
414.02
1.8111
411.79
1.7722
409.38
1.7425
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124
Refrigeration: Theory And Applications
Appendix: Physical Properties of Refrigerant R134a
Table A2: Properties of Superheated Refrigerant R134a – continued
T
P = 0.1 MPa
P = 0.2 MPa
P = 0.3 MPa
P = 0.4 MPa
h
s
h
s
h
s
h
s
°C
kJ kg-1
kJ kg-1 K-1
kJ kg-1
kJ kg-1 K-1
kJ kg-1
kJ kg-1 K-1
kJ kg-1
kJ kg-1 K-1
20
420.31
1.8874
418.33
1.8259
416.24
1.7876
414.01
1.7584
25
424.55
1.9017
422.67
1.8406
420.7
1.8027
418.62
1.774
30
428.82
1.916
427.04
1.8551
425.17
1.8175
423.22
1.7893
35
433.14
1.9301
431.44
1.8695
429.67
1.8323
427.83
1.8044
40
437.49
1.9441
435.87
1.8838
434.19
1.8468
432.45
1.8192
45
441.88
1.958
440.33
1.8979
438.73
1.8612
437.08
1.8339
50
446.3
1.9718
444.83
1.912
443.31
1.8755
441.74
1.8484
55
450.77
1.9855
449.36
1.9259
447.91
1.8896
446.41
1.8628
60
455.28
1.9991
453.92
1.9397
452.53
1.9036
451.11
1.877
65
459.82
2.0127
458.52
1.9534
457.19
1.9175
455.83
1.8911
70
464.41
2.0261
463.16
1.967
461.89
1.9312
460.58
1.905
75
469.03
2.0395
467.83
1.9805
466.61
1.9449
465.36
1.9188
80
473.7
2.0528
472.54
1.9939
471.37
1.9585
470.17
1.9325
85
478.4
2.066
477.29
2.0073
476.16
1.9719
475.01
1.9461
90
483.14
2.0792
482.07
2.0206
480.99
1.9853
479.88
1.9597
95
487.92
2.0923
486.89
2.0337
485.85
1.9986
484.78
1.9731
100
492.74
2.1053
491.75
2.0468
490.74
2.0118
489.72
1.9864
105
495.67
2.0249
494.68
1.9996
110
500.63
2.038
499.68
2.0127
115
505.63
2.051
504.71
2.0258
120
510.67
2.0638
509.78
2.0387
125
515.74
2.0767
514.88
2.0516
130
520.85
2.0894
520.02
2.0645
135
140
-20
-15
-10
-5
0
5
10
15
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125
Refrigeration: Theory And Applications
Appendix: Physical Properties of Refrigerant R134a
Table A2: Properties of Superheated Refrigerant R134a – continued
T
P = 0.1 MPa
P = 0.2 MPa
P = 0.3 MPa
P = 0.4 MPa
h
s
h
s
h
s
h
s
°C
kJ kg-1
kJ kg-1 K-1
kJ kg-1
kJ kg-1 K-1
kJ kg-1
kJ kg-1 K-1
kJ kg-1
kJ kg-1 K-1
20
411.61
1.7339
25
416.4
1.7501
414.01
1.7291
30
421.16
1.7659
418.96
1.7455
416.6
1.7269
35
425.9
1.7814
423.86
1.7616
421.69
1.7436
419.37
1.7268
40
430.63
1.7967
428.73
1.7772
426.72
1.7598
424.59
1.7436
45
435.37
1.8117
433.58
1.7926
431.71
1.7756
429.74
1.7599
50
440.11
1.8265
438.43
1.8077
436.67
1.791
434.84
1.7758
55
444.87
1.8411
443.28
1.8266
441.62
1.8062
439.91
1.7914
60
449.64
1.8555
448.13
1.8373
446.57
1.8212
444.95
1.8067
65
454.43
1.8698
453
1.8518
451.52
1.8359
449.99
1.8217
70
459.25
1.8839
457.88
1.8661
456.47
1.8505
455.03
1.8365
75
464.09
1.8979
462.78
1.8803
461.44
1.8649
460.07
1.851
80
468.95
1.9118
467.7
1.8943
466.42
1.8791
465.12
1.8654
85
473.84
1.9256
472.64
1.9082
471.42
1.8931
470.18
1.8797
90
478.76
1.9392
477.61
1.922
476.44
1.907
475.25
1.8937
95
483.7
1.9527
482.6
1.9356
481.48
1.9208
480.34
1.9076
100
488.68
1.9661
487.62
1.9492
486.54
1.9345
485.45
1.9214
105
493.69
1.9795
492.66
1.9626
491.63
1.948
490.58
1.9351
110
498.72
1.9927
497.74
1.9759
496.74
1.9615
495.74
1.9486
115
503.78
2.0058
502.84
1.9892
501.88
1.9748
500.91
1.9621
120
508.88
2.0189
507.97
2.0023
507.05
1.988
506.12
1.9754
125
514.01
2.0318
513.13
2.0154
512.24
2.0011
511.34
1.9886
130
519.18
2.0447
518.33
2.0283
517.47
2.0142
516.6
2.0017
135
524.37
2.0575
523.55
2.0412
522.72
2.0271
521.88
2.0147
140
529.6
2.0703
528.81
2.054
528.01
2.04
527.2
2.0277
145
533.32
2.0528
532.54
2.0405
150
538.67
2.0655
537.91
2.0533
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126
Refrigeration: Theory And Applications
Appendix: Physical Properties of Refrigerant R134a
Table A2: Properties of Superheated Refrigerant R134a – continued
T
P = 1.8 MPa h
P = 2.0 MPa s
-1
h -1
-1
s -1
kJ kg-1 K-1
°C
kJ kg
kJ kg K
kJ kg
-20
-15
-10
-5
0
5
10
15
20
25
30
35
40
45
50
55
60
65
430.33
1.7095
70
437.07
1.7293
432.06
1.7086
75
443.48
1.7479
439.12
1.7291
80
449.67
1.7655
445.77
1.7481
85
455.71
1.7825
452.17
1.766
90
461.63
1.7989
458.38
1.7833
95
467.47
1.8149
464.47
1.7999
100
473.25
1.8305
470.45
1.816
105
478.98
1.8458
476.36
1.8318
110
484.68
1.8607
482.21
1.8471
115
490.36
1.8754
488.02
1.8622
120
496.02
1.8899
493.8
1.877
125
501.67
1.9042
499.56
1.8916
130
507.32
1.9183
505.31
1.9059
135
512.96
1.9322
511.04
1.9201
140
518.61
1.946
516.78
1.934
145
524.27
1.9596
522.51
1.9478
150
529.93
1.9731
528.24
1.9614
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127
Refrigeration: Theory And Applications
Appendix: Physical Properties of Refrigerant R134a
Figure A1: Pressure-enthalpy diagram of R134a refrigerant
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128